Yes lel its for every move...
Why does the engine’s search depth reset to 0 after every move?
That would only work if the player plays one of the best moves. If they play a move the engine didn't calculate, the engine has to do the calculation all over again

I had a similar issue when logged in as my second account from <a href="https://writemyessay.nyc/">https://writemyessay.nyc/</a> with scmattwell username

No.
The engine doesn't look at EVERY move. Moves get pruned out of the search tree if the eval of that branch drops too low.
If the engine didn't re-calculate after every move, any move that had been pruned out would STAY out, even if making moves and pushing back the search horizon would change the eval that had caused it to be pruned in the first place.
Wouldn’t it save time if the engine looks for the best moves on the starting position until - let’s say - depth 30, and then after a move has been played, the engine picks up the analysis where it left off previously? Then in order to reach depth 30 again, it only has to calculate one more depth, right? I find it quite annoying that the analysis of the chess.com’s stockfish engine calculates an entire position to a certain depth, only to have the analysis be redone on the next move.