Online chess areas like lichess and chess.com absolutely have automated cheat detection which they consider along with with reports in automated banning of accounts. They consider not just whether the player is playing the excellent moves (something common at any level and very common at high levels), but also how a deep search is needed to evaluate that move, whether other obvious moves were available, how long was taken to play the move, if the position is common, etc. When these serial cheaters are banned, the sites even refund rating points to everyone who lost to them.
However, the issue of isolated cheating incidents is still a big deal, even if the serial obvious cheaters can be detected.
So maybe my only novel suggestion is running lichess (or equiv) live in parallel. Something livestream viewers could also help with.
And I hope someone's replaying historical games.
"how a deep search is needed to evaluate"
Of course. Obvious now that you mention it.
I assumed different programs would make different suggestions. So overseers would want to run a few programs to see if any matched the player's gameplay, style, etc.
Probably the last time I played chess was on an IBM PC XT. The quality of misc game engines varied widely. Of course there's probably been a convergence since.
So you can set some engines not to pick perfect moves but to pick moves consistent with a particular rating or style...
It could be modulated based on opponent, but does not have to be.
That's the next generation of chess engines - AlphaZero trounced Stockfish in a match of 100 games with 28 wins and 72 draws and not a single loss. And if you decrease the power a little bit (take an earlier generation), it makes significantly more human-like moves than Stockfish.
Re-running the games (especially to check for new techniques that aren't public at the time of the event) would be in the same spirit.
In the case of blood tests, there is a cat and mouse game of changing how the drugs are administered or other chemicals in the blood that reduce the effectiveness of the tests. Later on the presence of those other substances may be used as motivation for re-testing a group of people.
No one strategy is sufficient.
Create a fleet of chess programs, with typical resource constraints (CPU, RAM, time).
Have the chess programs replay recorded games.
Compare the suggested moves with the player's actual moves.
Divine some kind probability that player is cheating.
Extra credit for replaying that player's history of games thru the same fleet. Was the player consistent? Were there spikes of cheating?
Until there's a better phrase, I'll call this "parallel construction".
It'd be neat to run the fleet of chess programs during live matches.
Caveat: I know nothing about chess, so someone is probably doing "parallel construction" for cheat detection.