Extend `ResponseCache` to pass a context object into the callback (#10157)

This is the first of two PRs which seek to address #8518. This first PR lays the groundwork by extending ResponseCache; a second PR (#10158) will update the SyncHandler to actually use it, and fix the bug.

The idea here is that we allow the callback given to ResponseCache.wrap to decide whether its result should be cached or not. We do that by (optionally) passing a ResponseCacheContext into it, which it can modify.