Linux Mint 22 user here, also getting away from Rhythmbox. Using the GUI in Strawberry ver.1.2.3, here are some observations for using a streaming radio playlist, generally following @ben2talk .
From a blank slate with no playlists loaded, add some streams using Playlist | Add Stream. You'll notice that the title populates with the URL.
Click on a stream in the Title field. Here you can rename the stream to something more human using F2 or context click and select 'Edit tag "Title" ...'
Now save the same playlist to someplace you can find them, saving these three formats:
Christmas1.xspf (the default playlist suggested by Strawberry)
Christmas2.pls
Christmas3.m3u
Open all 3 files in a text app and observe their structures. Of the 3, only Christmas2.pls properly saves the renaming changes done above. Neither the XSPF nor M3U files save the Title changes, and if you reopen those playlist types (with or without tagging them as starred Favorites), the URL repopulates the Title field and you have to do it all over again.
The suggestions here for making changes to the M3U file work good to preserve your edits for that type of playlist. They may present differently in the GUI when compared to the sticky changes in the PLS file (you'll have to fiddle with the M3U #EXTINF and other directives to see what works best for you), but at least the work is preserved when you load the playlist. Again this all needs done by changing the M3U text file directly since the F2 GUI changes only stick for the PLS file.
Strawberry's default XSPF is in structured XML and I haven't dug into manual solutions for that.
As for direct modifications to the Radio tab offerings, if SQL is still the main Strawberry data backend (see @OriNOVet and this forum "Moving collection/config") there may be some opportunity. Christmas wish list to self: Dust off my rusty SQL and XML chops and look under the hood.
+1 for SomaFM. Great stuff.