Files corrupted after converting HFS+ volume to encrypted APFS

There are multiple challenges with the process you have gone through.

First of the entire premise of converting the drive seems to be a bad idea. You're using Time Machine for backups and want to convert the drive to APFS. But Time Machine doesn't support APFS at all - so even if you get the drive converted fully and correctly, then it won't work with Time Machine afterwards.

Regarding backup process: This process is indeed slow (or at least time consuming). There's no real way of telling macOS to speed things up, but you can ensure that the computer hasn't got much else to do. I have also seen that simply moving the mouse pointer around a little has a positive effect on the speed. Note that you can use the drive as usual while it is encrypting, and there's nothing that will be "fixed" by the drive finishing encryption.

You ask if the corruption occured due to a bug in APFS encryption. While it is possible, it doesn't sound very likely no. Most likely you had a pre-existing problem.

Whether or not you can recover data from the drive is impossible to say from your question. You can use various recovery tools and/or third party recovery services, they might be able to recover some of your data - but there are no guarantees.

All in all I think your experiences indicate that you have a hardware problem with your drive. I would suggest immediately shutting down your computer (you should really have done this a week ago when the problems started, but that's too late now). After shutting it down, use a different computer to take a bit-for-bit copy of the drive contents. Then run your data recovery programs, etc. on the copy instead of the original drive.

If you end up wiping the drive and starting over, I would suggest very thoroughly testing the drive before assuming it works. Again, it could very likely be a hardware problem with the drive.