I am not a modder, I am just a gamer. So, I recommend using mods, which can transfer your colony (map and all items, pawns and buildings on it) to new save game.
There 2 mods (known to me) which can do the job:

1. Save Maps (Continued)
   Supports 1.6 since 30.07.2025
   https://psteamcommunity.yuanyoumao.com/sharedfiles/filedetails/?id=2916523481
   
2. Map Saver
   Does not support 1.6 (as of 31.07.2025)
   https://psteamcommunity.yuanyoumao.com/sharedfiles/filedetails/?id=3354735289

If in your old save game you have mods which are not updated to 1.6, you may want to try this mod:
Mid-Save-Saver Continued
https://psteamcommunity.yuanyoumao.com/sharedfiles/filedetails/?id=3261311100

My guide preserves more than just your colony as it just adds missing things (biomes, asteroids, etc.) to your existing save game. I'm just letting you know that you have a choice of ways to migrate your colony to 1.6 / Odyssey.

In this guide we are going to generate (create) same world as in existing saved game. And than copy new world data (with new biomes) to the old save file. By doing it we will add new biomes to your old world/planet. Here is a compare screenshot:

Load your old save file from RimWorld 1.5 in RimWorld 1.6 and saved it. So, the game updates what it can. We are going to work with this updated file.

We are going to create a new world (planet) with the same seed and same globe coverage. Doing so will prevent errors with quest and settlement locations. With a different seed neighbor settlements or even your settlement may turn out to be in the middle of inaccessible area (ocean/sea).

Here are some ways to get world seed and globe coverage:

Vanilla way. Load the colony you want to transfer, go to world map, click any tile, in the left bottom corner press "Planet" button and write down the seed. Here is a screenshot:

Notepad way. Go to save folder, open save file with notepad, find XML "<seedString>" and "<planetCoverage>" tags. In this case planetCoverage is raw number (N/100%, e.g. 50% / 100% = 0.5).

Note: In my case seed is "PAXMA12" and globe coverage is 50% as you can see on the screenshots. Also, screenshots contain Cyrillic characters coz English is not my main language.

Now, as you know the seed, create a new colony to generate new planet (world) with this seed. Choose same globe coverage as it was in old save file. Don't bother with other settings like storyteller, difficulty, map size, factions, pollution, starting location, starting colonists and other. Just paste your seed, choose globe coverage and click next, next, next.

When you will be in game, make save file (save the game). Let's name it "new_world".
So, now you must have at least 2 saves (save files). One is your old saved game (from 1.5) and a new one ("new_world") which you just created.

Note 1: My new world had different factions and this did not affect process of transferring.
Note 2: You may choose globe coverage higher than it was in old save file. Looks like RimWorld will just delete extra (unnecessary) data.

You can open saves folder via the game itself. Go to "Options" -> "General" -> press "Open" button on "Save data folder" row.

On Windows your save files are usually in folder:

Now you will have to work with XML (save) files via some text editing program (e.g. notepad). I highly recommend using Notepad++ or some other notepad-like program which understands XML syntax and can fold XML tags. With these features the transferring will be easier. I will assume you use Notepad++.
Your old save file may be 100 MB (or even bigger) in size! That's a lot of text, and some text editing programs will stuck for some time trying to load all these text. Switching between these big files may freeze notepad for some time, so do not hurry and wait.

Backup your old save file! I prefer to work with a copy of original file. If something goes wrong, I can just make another copy of original file and shoot another try.

We are going to copy some world data from "new_world" save file to the old save file. Open both files in Notepad++. It may take a while to load, just wait.
Once both files are loaded in notepad, switch to "new_world" file and search (Ctrl+F) for "<tileBiomeDeflate>" tag. You will have two of them, but you want the 1st one (with a lot of lines of gibberish past the tag itself). Here is a screenshot as example:

Fold "<tileBiomeDeflate>" tag by clicking little square button with minus sign near the line numbers. Here is a screenshot (red arrow point to folding button):

Select "<tileBiomeDeflate>" tag with some extra characters on the next line (those wide spaces are called "tabs") and hit Ctrl+C (copy whole "<tileBiomeDeflate>" tag to clipboard). Here is a screenshot of how I did this:

Now switch to the old save file. Search (Ctrl+F) for "<tileBiomeDeflate>" tag (same one with a lot of characters) and fold it. Select the same range with same amount of extra characters on the next line and hit Ctrl+V (paste new "<tileBiomeDeflate>" tag from clipboard). Notepad++ will unfold the tag coz of pasting - that's okay. Also, in my case Notepad++ shows orange vertical line near line numbers indicating that those lines were changed. Here is a screenshot after I pasted new "<tileBiomeDeflate>" tag to the old save file:

https://psteamcommunity.yuanyoumao.com/id/Cyllin and https://psteamcommunity.yuanyoumao.com/id/iDaIRiUzZ reported that they had to copy additional tags to resolve issue with missing features of RimWorld 1.6 (v1.6.4543): abandoned bases, ruins and factories with new layouts, vents, etc.
Cyllin recommends to additionally copy following tags:
The process is the same as with "<tileBiomeDeflate>" tag. Locate the tag in new save, fold it, copy with some extra characters on the next line and paste it over the same tag in old save.

---

After you done copying new data to old save file, save (Ctrl+S) edited save file (old save file) to RimWorld's save folder.
Start the game and load edited save file.
Go to world map. And there should be new biomes (from 1.6 / Odyssey).

If your world is missing asteroids or has only 1 orbital platform of traders guild or other issues, see next sections.

kb3bus (https://psteamcommunity.yuanyoumao.com/profiles/76561197998966982) reported that his world does not have asteroids and offered a solution to fix this issue.

1. Open both edited save file (old save file) and "new_world" save file in Notepad++
   
2. In "new_world" save file find "<li Class="BasicAsteroidMapParent">" tag. There many of them, but you want 1st one.
   
3. Fold every "<li Class="BasicAsteroidMapParent">" tag, select all of them with extra characters on the next line and hit Ctrl+C (copy asteroids data to clipboard).
   
4. Switch to edited save file (old save file) and search for "</worldObjects>" tag. There are 2 of them, but you want the 1st one. Make a new line right above "</worldObjects>" tag. Here is a screenshot:
   
5. Paste (Ctrl+V) asteroids data on the new line and then delete empty line between last asteroid data and "</worldObjects>" tag. Here is a screenshot of final result:
   

• Save (Ctrl+S) edited file and load it in the game. Asteroids should be on the orbit.

Looks like old save files loaded in 1.6 / Odyssey have only 1 orbital platform (owned by traders guild). While new colonies (new save files) have more orbital platforms depending on globe coverage:

• 30% globe coverage = 5 orbital platforms
  
• 50% globe coverage = 9 orbital platforms
  
• 50% globe coverage = 13 orbital platforms

To add missing orbital platforms:

1. Open both edited save file (old save file) and "new_world" save file in Notepad++. "new_world" save file must have same or higher globe coverage than your old save file.
   
2. Switch to "new_world" file and search(Ctrl+F) for "<def>SpaceSettlement</def>".
   
3. Fold "<li Class="Settlement">" tags which have SpaceSettlement under them. There should be many of them (e.g. 9 if your globe coverage is 50%).
   
4. As your old save file already has 1 orbital platform copy rest, skipping the 1st SpaceSettlement. Select them with extra characters on the next line and hit Ctrl+C (copy SpaceSettlement data to clipboard).
   
5. Switch to old save file and search for "<def>SpaceSettlement</def>". Under it look for "</li>" tag and make new line after it like this:
   Notice "<faction>Faction_337</faction>" tag. You will need number ("337" in my case, you may have different number) from it later.
   
6. Paste (Ctrl+V) SpaceSettlement data on the new line and then delete empty line between last SpaceSettlement and next tag. Here is a screenshot of final result:
   
7. Now look for your 1st SpaceSettlement. You have to replace number in "<faction>Faction_NuMbEr</faction>" tag in ALL new SpaceSettlements with number from your original SpaceSettlement (which pre-existed in save file). In my case I have to replace "Faction_17" with "Faction_337" in all new SpaceSettlements. Here what I had (I selected text on the screenshots to focus your attention):
   And here how I replaced faction number:
   
8. Save (Ctrl+S) edited file and load it in the game. New orbital platforms should be on the orbit.

https://psteamcommunity.yuanyoumao.com/id/iDaIRiUzZ/ reported that he had problems with landmarks. Some landmarks exist without a marker, and some markers lead to plain world cells without landmarks.
So, inspect your edited save before playing!
If you see landmarks and markers mismatches, you can fix it by copying new landmarks from "new_world" to your edited save file.To do so:
Don't forget to backup your save file!

1. Open both edited save file (old save file) and "new_world" save file in Notepad++
   
2. Find "<landmarks>" tag. There are 2 of them, but you want 1st one.
   
3. Fold "<landmarks>" tag in "new_world" save file, select it with extra characters on the next line and hit Ctrl+C (copy landmarks data to clipboard). Here is a screenshot of how I do it:
   
4. Switch to edited save file (old save file), find 1st "<landmarks>" tag, fold it, select the same range (with extra characters on the next line) and hit Ctrl+V (paste copied landmarks data from clipboard). In my case Notepad++ shows orange vertical line near line numbers indicating that those lines were changed. Here is a screenshot:
   
5. Save edited save file and load it in RimWorld. Check again if there are any landmarks and markers mismatches (they should be gone).

P.S. I tried to find landmarks and markers mismatches in my updated world (old save file updated with new world data), but I did not find any.

Map of your base will not change. That means you will not see some new map generation features (like ice walls which 1.6 brings) in your colony. To solve this you can create a new base (so RimWorld will generate a new map with features from 1.6) and transport all items and pawns there (via caravans and/or transport pods). Then abandon your old base.

Also, I tried this old guide: https://www.reddit.com/r/RimWorld/comments/hthh3d/guide_relocate_your_colony_to_a_new_map_without/
But game glitches (unplayable) right after loading edited save file.

Any improvements and corrections to the guide are welcome. Write them in the comments :)