Replace FastAPI background_task usage with pydocket

[desertaxle]

This PR introduces pydocket as a dependency to replace our FastAPI background_task usage. Using Docket will preserve the default behavior where background tasks that shouldn't block API responses are run in-memory, but gives users the option to use Redis for more durable execution of those background tasks.

[codspeed-hq]

CodSpeed Performance Report

Merging #19295 will not alter performance

_{Comparing integrate-docket (2a1df38) with main (3cc4d69)}

🎉 Hooray! pytest-codspeed just leveled up to 4.2.0!

A heads-up, this is a breaking change and it might affect your current performance baseline a bit. But here's the exciting part - it's packed with new, cool features and promises improved result stability 🥳!
Curious about what's new? Visit our releases page to delve into all the awesome details about this new version.

Summary

✅ 2 untouched