External hard drive for Time Machine keeps running; Disk Utility exit code 65

New (Dec.) MacBook Air (M1, 2020), Big Sur 11.6.3, New (Dec.) Western Digital HDD, originally formatted by this laptop for Time Machine. It works fine for backup, file index is visible, Time Machine can be entered, etc. Problems: (1) HDD will not stop running after TM backup, even after 15 minutes or more (light is on, drive is humming; sometimes light is blinking and drive is humming); eventually it does stop, but when I try to eject it, it starts running again for another long while. Is this normal and I should ignore it, or why does it keep running endlessly? (2) With Disk Utility First Aid, the drive itself checks fine, almost instantly. The "container" and the Time Machine volume both error out with exit code 65. All the online help seems to be about "error 65" in other settings, but it seems like this too may be "ignorable"? But it does mean I can't run Disk Utility on the HDD, which I've taken to doing once a month due to problems with past Time Machine disk drives always getting gummed up on older iMac and earlier MacBook Pro. Suggestions? Thanks!