Migration Assistant fail
Here are a few notes which might help you. They wouldn't fit all in a comment, so I took the liberty to write half an answer.
Design

Anyone have any idea what may have gone wrong, so much so that
absolutely nothing happened after a good half hour of 'being busy'?

I've had a similar experience almost 10 years ago. From your description, it doesn't seem that Time Machine has changed much since:

Time Machine uses incremental backups in order to save disk space. Files are described by how they have changed over time. In order to restore a file at a given timestamp, diffs are applied on top of each other, starting at the original state of the file.
Time Machine uses hard links for folders, which are not supported by other macOS programs or by Linux.
Time Machine doesn't seem to check the integrity of the backups until they are needed. If any diff, any file or folder gets corrupted, Time Machine does not seem to notice.
During a migration or a recovery, the whole process stops after the first error. One corrupted file seems to be enough to cancel the recovery.
If the recovery process fails, no file gets copied at all, not even the files which have been processed before the first error.

All the above points, together, make for a brittle design. If anything goes wrong, your backup becomes useless, and cannot be read, as is, by any other standard software.
&quot;There's no step 3&quot; doesn't help much when step 1 &amp; 2 fail miserably.
Solution?
Your data, or at least a part of it, is probably still readable somewhere on your Time Machine drive.
I wrote a script in order to get my data back, but cannot find this script anymore. I remember it used ruby, cp -avX, ditto and chmod in order to parse the data and restore as much as possible.
There are more recent solutions, though. It seems that they use Linux and either bash or python. More info here. One of the scripts, copy_from_time_machine.py seems promising.
Good luck!