Use ReactDOM Test Selector API in DevTools e2e tests (#22978)

Builds on top of the existing Playwright tests to plug in the test selector API: https://gist.github.com/bvaughn/d3c8b8842faf2ac2439bb11773a19cec

My goals in doing this are to...
1. Experiment with the new API to see what works and what doesn't.
2. Add some test selector attributes (and remove DOM-structure based selectors).
3. Focus the tests on DevTools itself (rather than the test app).

I also took this opportunity to add a few new test cases– like named hooks, editable props, component search, and profiling- just to play around more with the Playwright API.

Relates to issue #22646