how to organize music on iPhone and computer ie, get them synched correctly

I've been building a music library on my Apple computer since 2009. That machine finally got too slow so I bought the new M1 machine in June of last year.

When I built my music library, 90% of my music was classical. When ripping a CD, iTunes always wanted to use the name of the orchestra or the musician for the artist, instead of the composer. Needless to say, this would make it very difficult to find a piece by, say, Mozart if the orchestra was listed as the artist, so I replaced every artist name on my library by the name of the composer as I added it.

When I transferred my music library to the new machine, it transferred exactly as it was on the old machine, that is artist name is the composer, as I made it.

When I loaded my music library on my iPhone 11, it automatically lists the name of the artist or orchestra instead of the composer, as it is on my iMac. I need to know the name of the musician or orchestra to find that piece. I've tried everything to get my Music library on the iPhone to the way it is on my computer Music library, but nothing works. iPhone wants to list it differently than it is on my computer, replacing my artist title (which is the composer) with the name of the players. I've tried everything to fix this but Apple won't let me. I don't know what to do. Any advice is gratefully accepted. I'm even willing to buy a piece of non-Apple software to fix this mess....