Is it correct that you are not using iCloud Photos?
Face ID is non-standard, and there is no metadata saved for it. Face ID does not transfer; each device does its own. There's little point in asking why Apple does it this way--certainly no one here knows why Apple does anything. Like everything connected with Apple, though, people seem free to guess and pass it on.
Using the Library on an external drive works well for a desktop Mac. But Photos does lots of work in the background, and so disconnecting the Library can cause problems for a laptop. We see that mostly with Libraries that are connected to iCloud, since there are more background processes then. I use iCloud for syncing, and I keep a smaller, Favorites Library as the System Library on the internal drive of my MacBook.
In the spirit of guessing and passing it along, I'm thinking that if i were you I would make a new small Library in the Pictures folder. When I was about to disconnect the external hard drive, I'd designate the internal Library as the System Library, and when I reconnected the external drive, I'd switch it back to the System Library. And I'd leave the external drive the System Drive and connected as much as possible. While it seems to me that Face ID and other scanning processes work on the non-System Libraries, they have less priority and it goes slower.
If your face IDs are "messed up," with people misidentified, then you should probably start over with the crazy ones. I mean, remove all the identities of anyone misnamed (not just on the mis-named pictures,) wait a while for Photos to catch up, and re-name those people with new names (like use Mac instead of Macintosh--you can change it later) to keep Photos from getting confused by old ID info.
By the way, I always include people's names in the Caption field. Important people get keywords. These things do transfer with the metadata, and they will survive changes to new OSs.
Good Luck!
