Hey again!

To start the final arc of my campaign, I want my players to realize that the puzzle they're putting together about the villain and the world is incomplete. To get the right information, I want to direct them to a Library of Lost Knowledge, a place theorized by wizards which exists at an intersection of the Ethereal and Material plane, perhaps at an old shrine to a Goddess of Knowledge and Truth.

The idea of the library is that it is a place where destroyed, hidden, or otherwise unknown knowledge is recorded. Its sort of like the library in ATLA, but leans a bit heavier into the concept of "lost" knowledge. For example, you might burn the lone copy of an ancient wizard's diary on the material plane, only for it to appear within this library in spectral form.

Now, I have an NPC set up who could know about the Library in theory, but how could my players actually physically find this place? I considered making the library "test" the players when they arrive, implying that other people have found it but were forcefully ejected, but I'm not sure what should clue them in to the actual location in the first place.

They'll be around 9th or so level at this point if all goes according to plan.

If it’s not too late, you should start seeding the idea very early. Third act plot devices can make it see like you wrote yourself into a corner, but if it’s been rumored for a while it feels less like a deus ex machina type of solution. Also, that can put the idea in their heads. It could even be something like a common phrase people use when the lose their keys or a sock “I guess it’s at The Library now”

How does the library, or its caretaker, feel about collecting all this stuff? Does it like the power that comes with all this knowledge, or is it saddened that everything it holds means one more forgotten piece of information on the prime plane?

I ask because that can help inform how they might get there. If I were a player, my first thought would be to find some rare piece of knowledge and destroy it to hitch a ride. If the library likes getting new things, it might welcome them with their sacrifice. If it doesn’t like it, the library would be upset. 
As a result, I might make there be 2 ways to get in, one way that’s favored by the library, and one it doesn’t like. Either way can get them there and get them what they need. The way it likes is harder to pull off, but makes life easier once there, and vice versa. 

As far as ways in besides the hitching a ride method, the easy one would be some homebrew ritual that opens a portal, where the ritual and its components can be as easy or difficult as you need to move the story along.
Or finding a higher level caster who can plane shift them there, so long as the players can provide the teleportation circle sigils (in the spell description).

Given my druthers, I would put it somewhere in the Shadowfell, mostly because of the association of the Raven Queen and memories. To get there one has to become a bit of lost knowledge themselves. To do so, make sure you have a secret, one that no one else knows. Murder of other keepers of the secret is traditional, but not necessary, then one simply begins to walk in the Shadowfell and deliberately get lost. Don't keep track of your surroundings, but keep going, eventually you will end up on the steps of the Library of Lost Knowledge. Putting on a blindfold hastens the process, but the Shadowfell is not a safe place. The Library cannot be found my magical or mundane means otherwise, except perhaps for a Wish spell. A Plane Shift targeting the Library will place you in a random Shadowfell location because the Library is the same 'distance' from every other point in that plane.