Aaaahhh, it's crazy how much this incident resonates with me! I've personally handled this exact same kind of outage more times than I'd care to admit. And just like the fine folks at Kagi, I've fallen into the same rabbit hole (database connection pool health) and tried all the same mitigations - futilely throwing new instances at the problem, the belief that if I could just "reset" traffic it'd all be fixed, etc...…
They would have some writes indirectly due to searches, say if someone chooses to block a search result. They’re also going to have some history and analytics surely.
But yeah it’s not obvious what should cause per search write lock contention…