The symptoms you describe are commonly seen with a failed or failing drive. Since Disk Utility cannot repair it, the next step would normally be to copy as much off as you can from the drive and then erase/reformat. But since you cannot access it from the finder, that might be impossible.
Or simply erase/reformat and restore from your backup.
I am hoping not to hear that you don't have a backup. If that is the case, you could investigate third party (non-Apple) utilities that claim to be able to repair APFS drives. Here is one, there are others
https://iboysoft.com/mac-data-recovery/apfs-data-recovery.html
Many of these have a free download with which you can test to see if it can recover files, but to actually recover them requires a purchase which is typically ~ $100.
I have had good experience being able to repair damaged HFS+ drives with commercial tools (as well as with Apple's Disk Utility), but have never had an APFS drive fail; however from what I have read, it is more of a long shot to successfully repair a damaged APFS drive.
If your external APFS drive is being used for Time Machine, I would simply obtain a new drive for Time Machine and erase/reformat the problematic one and then use it as a second Time Machine drive. Time Machine will alternate between the two and then you have another layer of safety.
If there are important files on it and you have no backup, you might have no choice but try some of the third party tools.