Inelegant, but did get back to a state where the two are talking. Tried a bunch of things (creating new iTunes library, reinstalling Music on the iPhone) which didn't work.
Ended up removing all music (~650 GB) from the iPhone. Settings was crashing when I tried to do it in bulk through the Settings -> Storage -> Music path. I removed some of the artists manually where I had a lot of content. With less (~300 GB) it didn't crash and completed the removal.
Today I'll sync some of it back. The first playlist is just finishing now so confident it should work.
Wish Apple didn't treat non-Apple Music subscribers as secondary. I am happy with managing my music myself but things like the 100K song bug (present for years now) remain discouraging. I bought a large iPhone for this specific use, too bad it's not built for purpose.