That’s a pretty accurate summary, GttSF.
But it still leaves me with my initial question: do you need to “touch base” at your library before a spell is truly known?
This could make sense in the fiction: you have the gist of the new spell, but you need to compare it to your prodigious collection of magical knowledge to make sure you have it right.
To be somewhat annoyingly punctilious, the rules say the library contains all of your known spells - therefore (maybe) a spell is not known until it is in your library?
Can a bloke:
Find a scroll.
Learn the scroll with Lore Master.
Scribe another scroll of that spell (which is now “known”) with Scholar.
Swap the spell from the scroll into the spellbook with Scholar.
Or is it:
Find a scroll.
Learn the scroll with Lore Master.
Return to your library and collate the spell to make it “known”. (no test)
At which point you can swap from your library OR a scroll using Scholar.
?