I got hooked on doing The New York Times crossword daily a few months after getting hooked on Wordle (which the NYT bought hoping to increase interest in its games section). I haven't gotten into the cryptics, but the US edition of The Guardian also offers that type of puzzle, at least to its subscribers.

As much as I love Sondheim (Sweeney Todd is my favorite musical), I think "devious minds" can get plenty of satisfaction from US-style puzzles. No doubt the NYT's crosswords have evolved since his writing, but they are often filled with wordplay and delightful themes, not simple definitions, in my experience.