"PRAGMA busy_timeout=1000;" is often helpful.

Inject requestids into a function name (generate a pass through dynamically one way or another) and attach a sampling profiler. Log slow requests and then find them in the profile.

I've seen the "root span" be the "page load" (i.e., the HTTP request that then initiates the websocket connection).

Ultimately a profile is a collection of stacks and you can convert into a greppable format and filter appropriately. I spent too much time on blog.philz.dev/blog/flamedu... at some point :)