Why does the analysis change after the best move?

I was analyzing the game of the century here en.lichess.org/OeY4qArY#48

At move 48 (24th move after black plays / check the analysis version ), white has a clear advantage and after playing the best move by the computer, black gets an advantage. Is stockfish broken?

It's because the engine was not given enough time to look deep enough into the position.
I recommend you to run stockfish on your local computer and check the results there so that the engine has enough time to think.