> I plan to move from Sequoia to Tahoe then use the photos library only on Tahoe moving forward. I don't use iCloud Photos.
Using iCloud Photos would still simplify this matter, even if you just used it to transfer the photos, then turned it off, but if you don't want that, the alternatives will still work.
den.thed posted links that walk through the process of moving a library to an external drive, and making it available on the other machine.
> Was I right in thinking that once I use the photos library on Tahoe via the external drive that there is some sort of file or mapping conversation that has to take place? So it might take some time to fully index the photos library?
Yes. With each new OS version (or, more specifically, major Photos.app version), certain old metadata is discarded and recreated in the new version's format. Specifically, the faces database is rebuilt (so you can filter photos by people, and the newer versions tend to be better at recognizing individuals), as are the maps (where photos were taken, based on embedded GPS coordinates), as well as text extraction (so you can search for text captured in a photo). This can take time (potentially many hours) depending on the size of your photo library.
If you subsequently move the photos back for any reason, the process is repeated on the older version (since it doesn't know how to use the newer format). This is the good reason to use iCloud Photos since it supports concurrent access across different versions, but it's not important to all people.