Give Nakamura a minute with Stockfish any two times of his choosing in each game, and he would have probably won the Candidates.
Heck, just give a good player a blunder alert that tells them after they have made a blunder that they have done so and it could make a big difference.
There were games in the Candidates where a player would make a blunder that would completely turn the game around if the opponent found the one move that exploited it, but the opponent didn't see it. The first player could have then saved themselves but had not yet realized they blundered so didn't. Then the other player realized what was going on and exploited the blunder.
The engine is so good that it often makes moves that are incomprehensible, setting itself up for an attack in n moves where n is often 10+.
If you did want to cheat (but what's the point?) a chrome extension that prevented you from making moves where you lost more then some certain amount of centipawns would be the way to do it.
I believe cheat detection is done partly by humans. Computers flag something as suspicious and then they show the suspicious moves to some grandmasters who might immediately say "no human would do that", or else "yeah that move looks weird but I could imagine someone making it", that type of thing. There was a youtube of Nakamura looking at such a position a while back. The person had a chance to sac some material in order to simplify to a trivially winning endgame, but instead carried out a ridiculously complicated maneuver that kept the material. Just the sort of thing a computer would do, and Naka pointed it out.
Thats exactly what those engines try to detect. If you are average player, but every time you start loosing you get significantly better, then there is great possibility that you are cheating. Thats whats looking through history gives you. It's about actually finding deviations from your usual behaviour.