So I decided to be brave and deleted everything from the external drive and start over with a Time Machine backup. It went very fast, about 10 seconds, which didn't seem right. But when I used Get Info to check the size, the top folder on the drive is 147 KB and the data file inside is 81.2 GB.
How could it have done 81.2 GB so fast?
Edit: I went further and erased the drive, then encrypted it as I had done before. I then set it as the Time Machine backup destination (oddly enough it did its own encryption and I used the same password) and started all over again. It took a while and again ended up with 81.2 GB. I'm confident in this backup, but how, when I had deleted the file before, did it also end up with 81.2 GB and did so in a few seconds???
There is a logical explanation, but it involves understanding APFS snapshots, and how Time Machine uses them, and what exactly you "deleted".
Each Time Machine backup after the first exists as an APFS snapshot on the backup volume. TM only copies filesystem objects that have changed since the previous backup. (Actually, I think that only the changed
portions of files are copied, at least in many cases, but that's not important here.) Some would say TM always does an "incremental backup" after the first. However, every "backup" looks and acts like a "full backup" when that particular backup snapshot is mounted and traversed with Finder or Terminal commands, or for a restore operation.
In your first paragraph quoted above, you "deleted everything," but don't say how you accomplished this. I think you deleted every APFS
snapshot, but you didn't erase all data on the drive (the data that exists outside of any APFS snapshot). I think the TM interface only allows deleting of backup
snapshots, and doing so doesn't format the disk. If I'm correct, this still leaves the 81.2 GB of data on the disk.
So, the "first backup"
data was still on the disk, but there were no backup snapshots. (Not sure what this would look like in the TM interface -- probably it looks like having no backups.) Then when you started a TM backup, TM only had to copy data that was different from what was (still) on the backup volume. This action created the first backup
snapshot (again, which LOOKS like a whole 81.2GB of data) and would be very quick. It only had to copy the differences between your boot drive and the data (still) on the backup disk.
Then in the last quoted paragraph, you "erased" the drive (with Disk Utility?), removing not only any snapshots but
also the data not in a snapshot. That backup "took a while and again ended up with 81.2 GB." This time, 81GB was actually copied and the duration was noticeable.
So hopefully this is an explanation of "how, when I had deleted the file before [first paragraph time], did it also end up with 81.2 GB and did so in a few seconds???"
If I understand the situation, I'd say you have a good backup and can continue building on it.