dillon1000/react

[DevTools] fix: keep search query in a local sync state (#34423)

When the search query changes, we kick off a transition that updates the
search query in a reducer for TreeContext. The search input is also
using this value for an `input` HTML element.

For a larger applications, sometimes there is a noticeable delay in
displaying the updated search query. This changes the approach to also
keep a local synchronous state that is being updated on a change
callback.