You don't even have to buy the songs on iTunes to have Apple stream them to all your devices. With iTunes Match (included with Apple Music subscriptions or available stand-alone) you can build a "cloud library" from local files: https://support.apple.com/en-us/HT204146
Watch out, iTunes Match and the Apple Music match service are subtly different: the former will match to (and failing that, upload, transcoding to AAC 256 if needed) DRM-free versions, while the latter will match to/upload for sure but downloading them on another device (or the same if you delete the source file) will get you a FairPlay protected file.
This is how I manage my music library, and other than the fact that iTunes Match could potentially 'eat up' a song you import into it if it matches to a different but similar-name/time track, it's been great.
I always keep a second copy of all my original rips just because I'm worried that kind of thing could happen—if not immediately, then later on when I sync a new computer and iTunes Match finds some new song that conflicts.
All iTunes songs are DRM free and available from the cloud on all devices that can run apple music. https://support.apple.com/guide/music/intro-to-the-itunes-st...