Reland "Add message handler to the floating workspace dialog"

This is a reland of commit 214a1479f69489c1b7c796cfbf4baaae6fd5dfbc

The state member variable wasn't initialized by default in
FloatingWorkspaceDialogHandler which broke the msan build.

Original change's description:
> Add message handler to the floating workspace dialog
>
> Add a message handler for the FW dialog and some functions,
> so it would be possible to change dialog states depending
> on the floating workspace service logic.
>
> Note: resources themselves will be added in a follow-up
> CL.
>
> Screenshot: screenshot/BsYSNsuWnYzo7RY.png
>
> Bug: b:411121762
> Change-Id: I029e2792c06e655591564bffcd1155834ee0799a
> Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6544148
> Reviewed-by: Andrey Davydov <andreydav@google.com>
> Reviewed-by: Antonio Sartori <antoniosartori@chromium.org>
> Commit-Queue: Michael Slutskii <slutskii@google.com>
> Cr-Commit-Position: refs/heads/main@{#1460611}

Bug: b:411121762
Change-Id: I3e35d433891f833c73653b4407e7925c0d6deb8b
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6553929
Reviewed-by: Andrey Davydov <andreydav@google.com>
Reviewed-by: Antonio Sartori <antoniosartori@chromium.org>
Commit-Queue: Michael Slutskii <slutskii@google.com>
Cr-Commit-Position: refs/heads/main@{#1461292}