Decouple browser test state observation from its modifier.

Removes issuing RPCs from the state observation, creating cleaner flow.

Speculatively decreases flakiness rate by:
* explicitly ceasing the observation of the browser state (since Reset and Define manipulate the same state but in opposite way),
* adding some space between starting browser state observation and issuing RPC that will change it,
* replacing adult page, as the current one seems to 503 often also contributing to flakiness (503 page is not the intended end-state)

Bug: 328036610
Change-Id: I3cb776c3d141891184cd59baa9b1b1eaee76b502
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5402480


Reviewed-by: Anthi Orfanou <anthie@google.com>
Commit-Queue: Tomek Jurkiewicz <tju@google.com>
Cr-Commit-Position: refs/heads/main@{#1280182}