While it will be of no comfort to you whatsoever, you are not alone. Many, including myself, have to "manage" their DRM-protected Apple Music Library from a Windows PC or a Mac.
Speaking of my own situation, the vast majority of my music collection is CD-based. For convenience when I'm away from home, or in the car, a significant proportion of my extended catalogue of titles has been legally "ripped" from CD by iTunes - and this library has been synchronised with my iPhone and iPad. As new titles are added - or if I change or restore a device - the PC is called into service to sync or restore the iTunes Library to the device. Just like you, I find this to be an inconvenience. That said, I understand and respect the reasoning behind the restriction that is imposed by Apple.
There are two potential methods to ease your current pain...
1) Subscribe to iTunes Match - Apple Support
This method initially relies upon your iTunes Music library - however, the iTunes Match subscription allows Music stored on your devices to be accessible from all of your devices via Apple Music. While this service is subscription-based - and might not recognise all Music within your collection - it may at least provide an alternative to the DRM-restriction that inhibits simple transfer of your music/mp3 titles.
2) If you are prepared to step beyond using the Music App on your Apple devices to organise and listen to your music collection, there is an alternative that will allow you to keep your music/mp3 titles saved on your device - and included within your iCloud (or other backup)...
Some third-party File Manager Apps can access and play music/media files, of various types, directly from local device storage, USB connected storage, or cloud storage services. Clearly, you are interested in storing your mp3 library on your iPad (or other devices) where it can be played.
Instead of synchronising your iTunes library with the iPad for playback using the Music App, consider copying your mp3 titles as they are to your iPad's local storage - such that they can be accessed using the iPad's Files App. To copy the files from your PC where they currently reside, you might:
a) install iCloud for Windows on your PC and use this to copy mp3 files initially to iCloud - from where you can use the Files App to copy them to your iPad's local storage, or
b) use the iTunes App on your PC to copy the mp3 files (as files) to the iPad. You should note that you are not synchronising your Music Library with the iPad - but will be copying the files "as files". The difference is subtle, but the objective is to keep the mp3 files outside of the DRM-restricted library that can be accessed by the iPad's Music App.
While the files can be "managed" using the Files App, you sill need a suitable File Manager App to play the mp3 files...
One such App that comes readily to mind (that I use daily for many other tasks) is FileBrowser Professional by Stratospherix:
https://apps.apple.com/gb/app/filebrowser-professional/id854618029
You would be well advised to review the extensive online Manual and help files to determine suitability for your needs.
https://www.stratospherix.com/products/filebrowserprofessional/filebrowser-professional-user-guide.php
You should note that there is no penalty to your iPad's available "storage space". The mp3 (or other) files occupy the same amount of storage. What's different is where the files are being stored within the iPad filesystem - and how these files are accessed. All files that are outside of the DRM-restricted storage space are included within your device backups.
I hope this additional information and understanding might offer some practical help in providing some alternative strategies.