Isn't that what Lichess already does, plus estimate difficulty based on which bot Elo is required to solve the position? (The OP's site doesn't have difficulty estimates but it's from A curated book so presumably that's captured in the puzzle number.)
There are some filters in lichess, but you can't easily combine them in lichess.
So you can filter problems for queen sacrifice or mate in 3 but not the combination of the two.
The second quote means that the puzzle rating is dynamic and changes every time someone tries to solve it (the puzzle gets points for losing / winning the same way the player wins/ loses rating for solving the puzzle. )
https://database.lichess.org/#puzzles
> Generating these chess puzzles took more than 50 years of CPU time.
> To determine the rating, each attempt to solve is considered as a Glicko2 rated game