This part is correct:
I thought this would be possible because, as indicated in threads like this (Location of database files and software ), it’s my understanding that LocalWP is supposed to save out the database to [site directory]/app/sql/local.sql
but as far I know, this part is not:
and when the site is launched, it uses that sql file to rebuild the database.
The database is dumped out to the local.sql file on shutdown (primarily for backup purposes, I suspect), but isn’t re-imported to the database on starting a site. In most cases, there isn’t a need to re-import it, as they should already contain the exact same database structure and data.
When you move the drive from one machine to another, it sounds like you’re moving the site files, but not the database files. The database files (not the local.sql dump file) are stored separately from the site files. Per the image linked in the thread you referred to (https://i.getf.ly/p9uQOZYl), you’ll see that on MacOS it’s within a site-specific folder under the /Users/[user]/Library/Application Support/Local/run/[site-folder]/mysql/data directory. I don’t know if moving those database files between machines will cause issues.
But, as you mentioned, you can always manually import the local.sql file to the database on each machine after starting the site in Local.
I know there have been threads in the past that discussed trying to work on the same site across multiple machines. I don’t know if any of them have had any real success, but perhaps there are relevant suggestions in those that might help you.