Reland "[bedrock] Match browser collection close with BWI did-close events"

This is a reland of commit 36d0f0ca9bc67a071b33a8f0cdb66e580f29981e

Original change's description:
> [bedrock] Match browser collection close with BWI did-close events
>
> Currently BrowserManagerService emits close events immediately before
> the browser instance is destroyed.
>
> However BrowserWindowInterface is closed earlier, and destruction
> happens asynchronously.
>
> This CL updates BrowserManagerService, and consequently the
> BrowserCollection APIs to match the close event propagation of their
> BrowserWindowInterface instances.
>
> Logic from ~Browser has been inlined into BrowserManagerService
> as these steps must be the last things run during Browser
> destruction - or immediately after Browser destruction.
>
> Follow up CLs will refactor these to address the existing TODOs.
>
> Bug: 431671320
> Change-Id: I3fd2783f40a774128b152b33cb4794aed1f7575b
> Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/7570170
> Commit-Queue: Tom Lukaszewicz <tluk@chromium.org>
> Reviewed-by: Glenn Hartmann <hartmanng@chromium.org>
> Cr-Commit-Position: refs/heads/main@{#1586192}

Bug: 431671320
Change-Id: Ia30b59b3b13a566a2e1d93c71412fea2235f4267
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/7586615
Reviewed-by: Glenn Hartmann <hartmanng@chromium.org>
Commit-Queue: Tom Lukaszewicz <tluk@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1586524}