Revert "[AvatarButton] Fix signin paused state not clearing on signout + cleanup"

This reverts commit 97e5f0c6015dfc996b4281fcd593e9f908c9366c.

Reason for revert: consistent crash across multiple platforms upon browser launch, b/331499330

Original change's description:
> [AvatarButton] Fix signin paused state not clearing on signout + cleanup
>
> Signin paused state was not active anymore, and signing out of Chrome
> did not trigger a state change. Listening to primary account change
> fixes the issue.
>
> Refactoring parts:
> - Cleaned up the StateManager code to only compute new state
> internally or by request of StateProvider implementations, to make
> sure all the states control the active state and updates properly.
> - Injected specific logic of some StateProviders from the
> AvatarToolbarButtonDelegate into the StateProvider itself, and
> give a way to retrieve the StateProvider from the StateManager
> to read the value, when that State is the button active state.
> - Removed the icon related updates from the StateManager as they
> should not alter the state.
>
> Bug: b:329802297
> Change-Id: I0728747601de816cfe477a1ad2356c1e4b6bebb3
> Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5380711
> Reviewed-by: David Roger <droger@chromium.org>
> Commit-Queue: Ryan Sultanem <rsult@google.com>
> Cr-Commit-Position: refs/heads/main@{#1278381}

Bug: b:331499330
Change-Id: Ifd0bd8e55fcccf511a0cbda63526e11a55a9e7f2
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5399659
Owners-Override: Tsuyoshi Horo <horo@chromium.org>
Auto-Submit: Di Wu <diwux@google.com>
Bot-Commit: Rubber Stamper <rubber-stamper@appspot.gserviceaccount.com>
Commit-Queue: Di Wu <diwux@google.com>
Cr-Commit-Position: refs/heads/main@{#1278775}