Music not purchased on iTunes will not transfer to new Mac running Catalina MacOS

Greetings all, so here's the deal. I have a mix of music on my old iMac both purchased and ripped from a lifetime of old CD's. I now have a new iMac Pro and have been trying to move my music over. I can get everything that was purchased from Apple across, thats a no brainer. However, everything that was not I can't get to move. It was suggested that I use my iPhone to transfer across, which I was able to move all of this non-iTunes music from the old iMac (Mojave) onto. And here is sits. I understand that the under the Finder (Locations) I can access my iPhone and can then "sync". I can see all the of the music I want to move when I do this but I can't get it to move. If I click on the "Music tab" and click on the "Sync music onto...iPhone". I'm faced with this warning: "Are you sure you want to remove existing music, movies, TV shows, and books from this iPhone and sync with this library? Music, movies, TV shows, and books synced to “Shawn's iPhone 11 Pro” from other libraries will be removed and items will be synced from this library." This sounds ominous, like I'm going to loose one or the other and not combine the two.

I have also read that I could go tot the "General" tab and under options choose to "Manually manage music..." When I hit "Apply" I get an equally ominous message that says: "Syncing “Shawn's iPhone 11 Pro” with this computer will replace media from another library on “Shawn-Patrick iMac. An iPhone can sync with only one computer at a time.” (Note that the name Shawn-Patrick iMac is the old iMac not the new one.)

Can anyone direct me to what I need to do to get all of this music to be consolidated into one place? I've also read several articles about people overwriting or losing their music all together.

Thanks,