Cheating is increasing significantly in Classical and Rapid

One reason that sometimes people might appear to be playing well above their level is actually due to the nature of chess and the fact that the game is both incredibly simple and complex at the same time.
The reality is that you can analyze chess at many different levels and, especially with attacks, sometimes the thing looks incredibly powerful but is actually a busted line if you play perfectly. Or, it looks like it can be beaten with thinking but it just happens that everything is positioned such that it cannot be. Most people do NOT analyze every line or even close to their main attack theme and so sometimes people look super strong but a chess engine will find a LOT of ways to counter. Conversely a stupid looking attack might end up being genius but it doesn't mean the player who made it was really thinking. They might just only have looked a couple of moves ahead, their opponent may have been looking many moves ahead and thought it wouldn't work, but maybe there is an engine line many moves beyond that which makes the original line the correct one. You just can't know for any given game what the thinking was.
Having said that, a way to look for cheating would be, do they do different things at different levels. Now I know some people have preferences for knights playing very quick games due to calculation issues vs bishops, but besides that, most people tend to play the same openings and they for sure know the same amount of "theory" for each level. After all, if you know some opening 10 moves deep it doesn't matter if you are playing rapid or blitz, you can do it in both. So a yellow flag would be playing very different openings at the two levels. Then there is the usual stuff... if there is are moves that you cannot really not do, an engine would still think for a while, a human would just make them. Now what people sometimes think of as cheating is some player thinking a long time on a critical move. This does feel like cheating but in reality it most likely is calculation. One way to consider if its cheating is to see if the next moves in the sequence are also now happening with a regular gap that indicates an engine might now be on. But its hard to figure it out. Lichess though can do more stuff like check if someone is looking into another window, or do much more data crunching - how different is the centipawn loss between blitz and rapid and classical and maybe even bullet (although given how often bullet is won on time this may not be that helpful as centipawn loss can blow up if you are sacrificing aggressively just to push the clocks)...

the engines (stockfish houdini)have poisoned online chess

Chess.com closes more than 800 accounts every day for cheating , lichess? www.chess.com/article/view/online-chess-cheating