I don't know. I imagine if someone was going to adjust the timing or targets of strikes in a war in response to a prediction market bet, or the decisions of a high-profile court case etc, they wouldn't say so in public the way the CEO of Coinbase did on that earnings call. It's pretty rare that someone would actually claim they're taking an action specifically with the purpose of altering the outcome of the prediction market bet, rather than giving some other reason. So even if it were happening, the only evidence I might expect to find would be suspicious prediction-market trades around low-probability events.

In situations like this, where you wouldn't expect to see evidence of something even if it were happening, you're basically left to make a judgement based on prior probability. So here that would come down to: is the financial incentive provided by the prediction market high enough relative to the decisionmaker's perceived risk and penalty of being caught? IMO, the answer is currently 'no' for most high-profile cases, but in a future where more money is riding on the bets, or where decisionmakers are insulated from consequences, that could swing to 'yes'.