For chess analysis, I recommend SCID vs PC. It turns out that chess-playing programs have standardized upon UCI (Universal Chess Interface), meaning any chess-playing program, (IE: Stockfish and Leela Chess) can interface with any UCI program (in this case, SCID vs PC). SCID vs PC can then be tuned to whatever you think is appropriate for review. Add the tablebases if you want perfect endgame analysis, or favor faste…
Lichess uses Stockfish 14+ NNUE compiled with WASM, so it should be essentially as fast as running it locally on your own machine. They don't expose as many of the tuning options, but that's not an enormous difference for most people. So no, it is just just some Javascript program. And as far as I know, essentially every modern chess engine uses a hashtable of positions such that transpositions are essentially free.…
Running Stockfish 30% to 40% slower for no reason at all, and with far less RAM / resources means that you'll get weaker analysis at slower speeds.
And those "tuning options" include tablebases, which would provably play perfectly (and Stockfish is smart enough to "think" with tablebases: if it can prove a won position with a tablebase, it won't bother exploring and will just report the mate-in-300 immediately)