How can I keep my MP3s on iMac with Apple Music?

Hi all.

Hopefully someone can shed some light on this.

I've been using Apple Music and iTunes since the beginning and I'm normally pretty good with it, but I am having an issue that I am struggling to understand.

This is what I am trying to achieve:

I have an Apple Music subscription. This is streamed to my iMac, iPhone and iPad. I dont download stuff from Apple Music.

I also have 50,000 mp3s that were on my iMac in Apple Music (from the iTunes days) and these also sync to my other devices (iPad, iPhone)

I had the assumption that it was uploading these 50,000 mp3s to the cloud so they were accessible everywhere and that they were staying on the iMac. Turns out they are not. Anything that gets uploaded (not matched, illegible or duplicate) is no longer in my iMac. I dont like this and have searched high and low to find a way to have them stay on my Mac locally.

Can someone help me please?

Cheers!

[Re-Titled by Moderator]

Original Title: Help with Apple Music Library