I am having this issue (with MacBook Air 2020 M1/Monterey 12.4).
I have 2014 and a 2018 MacBook Airs and have never had this issue with either of them (and still don't...).
I periodically connect my Seagate 1TB External Hard Drive to manually run back-ups - never had this issue until I got the 2020 MBA. AS I TYPE THIS, I am backing up my 2014 MBA to the SAME Seagate that I just spent the last three hours trying to back-up my 2020 MBA to, with no success (every time the new one prepares to run a backup, it ejects - cancelling the backup....but the external hard drive is still visible in Finder. This actually makes no sense.
I bought a new cord, thinking that was the issue. No luck. Tried using an Apple adapter to connect hard drive to MBA. No luck. (And my original cord still works to backup my older MBAs). Ran First Aid; reformatted external hard drive; changed power settings....tried everything. No luck. Would really like to hear if anyone has found a solution that works for the 2020 MBA with M1.