Previously, navigating on a website with the DevTools inspector open would make it not show the new HTML tree and not properly update. It could only be fixed by disconnecting the DevTools client and connecting again.

Now navigation correctly updates the inspector, both for the same page and external navigation. We now get the BrowsingContextActor through the WatcherActor, which remains the same across navigations (unlike BrowsingContextActor). As a result, many actors were changed to have a reference to the watcher instead.

This is also a first step in cleaning the actor dependencies and avoid registration issues.

Know issues (better addressed in followups):

• After navigating within the same domain, new console messages don't appear in the console. They appear again once navigating to a different domain.
• The console messages are not cleared when navigating.
• Navigating quickly through multiple pages can trigger an "already mutably borrowed" panic. This is an existing issue that is tracked in devtools: Panic with ActorRegistry already mutably borrowed #45055
• After reloading, the HTML tree is not correctly displayed. A workaround is to manually navigate.

Testing: ./mach test-devtools
Fixes: #41848
Fixes: #42603
Part of: #39862
Part of: #45055