You can use almost any MP3, so long as it's a constant bitrate. Bandai-Namco specifically calls out:

• Sampling Frequency: 32000 Hz / 44100 Hz / 48000 Hz
  
• Bit Rate: 96 kbps / 112 kbps / 128 kbps / 160 kbps / 192 kbps / 224 kbps / 256 kbps / 320 kbps

If it's a variable bitrate, or some odd bitrate that isn't on that list, it may not appear. If it's any other format (.wav, .ogg, .flac, .m4a, etc) it won't appear. So that means if you say, bought a song from iTunes, you'll need to find some way to convert it first.

Steam user VISITOR9x uploaded a great compilation, it's in the parent of this thread.
They've edited the tracks to cut down on slow sections and intros, and the latest (as of when I wrote this) has been volume normalized.
The thread can be found here: https://psteamcommunity.yuanyoumao.com/app/1909950/discussions/0/604165686037578099/

For Windows, Bandai Namco provided a guide. In short, you'll want to place your files in: C:/Users/<your windows username here>/AppData/LocalLow/Bandai Namco Entertainment/SRYMUSIC



Copy your MP3s there, no directories. Pay attention, this is not in the SUPER ROBOT WARS Y directory.


Also note that if you used the archive linked in the first section, the directory in there is "SRWMUSIC", this MUST be SRYMUSIC

When you've got your files extracted, this is what you'll see

First, enter Desktop Mode in your Steam Deck (Steam menu > Power > Switch to Desktop). If you've got a Bluetooth mouse and keyboard, working in desktop mode is a lot easier, but they're not strictly required.

After that, the process here is almost identical to Windows, but a slightly different path. When Steam duplicates files from Windows user files on Steam Deck, there's a shared path. This is always at "/home/deck/.steam/steam/steamapps/compatdata/<appid>/pfx/drive_c/users/steamuser"

Open Dolphin, and in the address bar past in the path:
/home/deck/.steam/steam/steamapps/compatdata/1909950/pfx/drive_c/users/steamuser/AppData/LocalLow/Applicaiton Data/Bandai Namco Entertainment


Create SRYMUSIC if it doesn't exist and past your files there Copy your MP3s there, no directories. Pay attention, this is not in the SUPER ROBOT WARS Y directory.


Also note that if you used the archive linked in the first section, the directory in there is "SRWMUSIC", this MUST be SRYMUSIC

When you've got your files extracted, this is what you'll see


Notes:

• This guide assumes you're running off the internal drive on the Steam Deck, I'm not sure if the path changes when running from MicroSD.
  
• To actually get files on the Steam Deck, it's probably easiest to just download them from the link earlier in the guide. You can also use a USB-C thumb drive or a microSD card (assuming you're not running the game from a card already)
  
• Apologies for the potato images in this area, I wasn't sure how to screenshot in desktop mode.
  
• It's overkill for this, but if you find yourself modding games on PC and Deck, there's an application called "SyncThing" that is really useful for keeping your mod directories synced up. I use it for Baldur's Gate III and Balatro.

Once you've got your files in place and you're in-game and have a save loaded (you can't do this from the main menu)


1. Go to Options Menu > System > Sound Settings, then select BGM Selection.


2. Choose the unit you want to modify. A green icon is an in-game track, here I'm editing Reideen


3. The line with the unit next to it is the default. This will play when you're not attacking with that unit or you're using a new attack that wasn't present during this step. Note that if an event plays that isn't specifically a combat thing, it will use the in-game song.


4. Change the "Sort Mode", this is Q/E on keyboard, or LB/RB on controller
5. If songs have an album set in their ID3 info, they'll be organized into albums. Select your song, preview it with the F key or Y button on a controller, and then confirm.


6. Now the icon is blue, indicating a custom song. If you want to set this for all attacks and the unit, press Esc on keyboard or Start on controller.
7. Back out to select another unit or to get back into the game.

You now have custom music.

Notes:

• You can only set songs for units and attacks you have unlocked. If you're in a combat map, you can only set songs for units actually present on the map too.
  
• In Super Robot Wars 30 (as well as X/V/T, I believe) you could just replace a song entirely, that's not an option in SRWY. As such, you can't set songs for events, you'll get the default in-game song.
  
• If a song doesn't play, you may have a corrupt file.