DevTools: Extension should start/stop recording scheduling profiler data

[bvaughn]

Wire up the Profiler's start/stop record button for the new scheduling profiler (#21866).

See this POC by @taneliang as a reference / starting point.

Note that we should probably not add "debugger" as a permission in the extension manifest, but as an optional_permissions that we request at runtime if someone tries to use the new profiler functionality.

[NishantChandla]

@bvaughn Can I take up this issue? Also, I am new here can you guide me how can I go about solving this. Thanks!

[bvaughn]

@NishantChandla You're welcome to work on this task if it interests you, but it would have to be an unguided effort. (I don't have bandwidth to guide anyone through it beyond what the description already states.)

This guide may help you get started:
https://github.com/facebook/react/blob/main/packages/react-devtools/CONTRIBUTING.md

[bvaughn]

This is not possible without adding a really pervasive permission, so see #22529 for an alternative.