Thank you for the example file @g-man-langley !
I've analyzed the issue and it's related to two different ways of storing the genre in the MP4 tag.
Mp3tag tries to use the gnre MP4 atom for genres that are part of the ID3v1 standard. This stores the index to the actual genre in this pre-defined genre list. For custom genres, it uses the ©gen MP4 atom, which is what Apple Music seems to expect now.
The file in question uses the gnre atom (ID3v1 genre index), which also doesn't seem to be supported by MinimServer.
I have not decided on a solution for this so far.