Can I run Protools 10 on the M1 MacBook Air?

Suggest, for all mentioned Applications and Plug-Ins that you verify if the Developers offer updates or upgrades to their software to make them work in Big Sur AND the New Apple Silicon M1 CPU

As for Time Machine Backups - In Big Sur the drive must be formatted as APFS ( New Apple Filing System ) and if the same dive is used in Big Sur - it will offer to Reformat the drive. One down, all the Old Time Machine Backups will be useless if every reverting to older macOS.

Once can always do a little work and see if your important applications etc would run on an older version of macOS like Mojave which still supports 32 bit applications and extension plus drivers. If that would work for your needs, Apple does offer Refurbished computers at a reduced price. Have purchased several and they are as good or better than new. Comes with a 14 Day Return Policy and 1 year Warranty. One I purchased has a Brand New Battery installed at time of purchase. Just be sure to check what version of macOS is installed at time of consideration. The version installed is normally Non-downgradable to older than what was installed. There is another seller of used Apple computers called Other World Computer ( OWC for short ). Very reputable outfit

Fast Answer NO !

The OS on New MBA M1 ( Big Sur ) is not allowed to be downgraded as per Apple Rules. Second point - The M1 CPU would not run anything less than Big Sur. The machine code to operate the M1 CPU would not understand the machine code in anything else ie Catalina, Mojave, High Sierra, Sierra etc.

As for not really answering you question - the Due Diligence rests with the User to research these thing out.