There is simply no way to pre-store any arbitrary long text because the possible combination is just tooo huge. It is like draw a bullseye where you arrow landed. You search any paragraph, it search existing index, if not found then save it and assign it a new index. Of course it may use some algorithms to optimize/decrease the space needed.

From it’s wiki page, https://en.m.wikipedia.org/wiki/The_Library_of_Babel_(website) ‘’’ The website can generate all possible pages of 3200 characters and allows users to choose among about 10^4677 potential pages of books. ‘’’

PS, I think again, indeed this actually does not need any storage, it can be URL to text encoding/decoding, the URL itself can determine/generate the actual text. And same for the opposite direction

No, you can run it on your own homelab just fine. If you don’t have it already, you just need a (usually free) dynamic subdomain so your instance have a normal URL instead of IP.