This is the most "efficient" way I found to get the maps to show on the Steam Workshop. It's stupid and requires a tremendous amount of workarounds, but at least it works, which is the intended result.
If anyone has ideas or suggestions on how to streamline the process, I'd gladly edit them in.

The base process was taken from this link (in Russian) which I've tweaked.
https://stmods.org/spintires/news/karti_v_masterskoy_steam_2016_03_10_by_khan/

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First things first, I'm going to assume that you have a Spintires map completed and ready for upload. This guide will only be covering the uploading process, not the map creation itself.

Step two, you will need to download SteamCMD, Steam's command line interface.
How to and install steps in the official Valve documentation.

Three, please note that both the .cmd and the .vdf files can be created and reopened with the basic Notepad program shipped with Windows, because they're essentially just plain text lines.

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Launch the Spintires Editor, right click on mods, create a new mod, right click on it and publish it. You can set the visibility to Friends Only for the time being, it doesn't matter.
The thing is that the Editor has direct connexion to the Workshop, allowing us to create a new item on the Workshop (even though it's an empty shell right now), in which we will be pushing the map files. Go into your Workshop items, find the empty item and note down its Workshop ID number.
You can do so by either enabling the Steam URL display in Stam settings, or simply by right clicking anywhere on the page and copy the URL to your clipboard. Extract the ID number and note it down somewhere, we will need it later.

Create a new folder at a location of your convenience, with the name you want.
This will be the folder exported to the Workshop, I suggest keeping the name simple and creating the folder in an easy to access place, because we're going to need the full path reference.
Inside that folder you need :

- a "levels" folder which contains the <level_name>.dds and <level_name>.stg files from the "levels" folder in the Spintires Editor.
- another folder which has the same name and content as the "prebuild/<level_name>" folder in the Editor (lots of .dds files and the "mud" file)
- the <level_name>.xml file found in "prebuild"
- a "preview.png" files which you obtain by converting the <level_name>.dds file into a .png
- a .vdf file which I will detail below

The name of the .vdf file doesn't matter, but you will have to reference it at the next step so again, keep it simple.
Content of the .vdf file (I'm using an image to keep the indentation intact) :


Additional notes on the .vdf :
- Visiblity 0 corresponds to public.
- I need to experiment more to see if some of those fields can be left blank. As it stands right now, the content of the .vdf will overwrite the existing name and description for the map, a bit annoying if you want to actually update your map after its initial release.

Outside of that export folder, I repeat, OUTSIDE, this is very important, create a file named upload.cmd with the line which follows. Keep the quotation marks where they are, do not include them if they aren't, and replace the brackets with your own data.
The "pause" instruction must be one line below the rest. Its sole purpose is to freeze the console so you can read the return values to know whether your upload suceeded or not.

"[path to steamcmd.exe]" +login [Your Steam login] [Your Steam password] +workshop_build_item "[path to your .vdf file]" +quit
pause

Double click on the .cmd file to run it. Steam will prompt you for your 2 factor authentication if you have it. Also note that the process will disconnect you from the regular Steam app, which you will have to restart once the process is complete.

If all went well, your map is now uploaded properly on the Steam workshop !

Please check out my other guide on how to load these maps downloaded from the Workshop, because just subscribing to them is not enough, users ned to edit some files to be able to see them in the game map selection screen.
https://psteamcommunity.yuanyoumao.com/sharedfiles/filedetails/?id=2954520351