Reland "Fix a regression in UrlHandlerAsh"

This is a reland of commit 39424a749aa23ac8865324d44c130203e63812e7
without changes. It was reverted before due to an unstable test,
which is now fixed.

Original change's description:
> Fix a regression in UrlHandlerAsh
>
> https://chromium-review.googlesource.com/c/chromium/src/+/4703969
> introduced a bug in UrlHandlerAsh because I had missed that we need
> SWA registration already completed in order to find the suitable SWA,
> not only when launching it.
>
> This change restores the previous, correct, behavior.
>
> Note that BrowserNavigatorTestChromeOS.OsSchemeRedirectSucceed, the relevant test, is still disabled due to a different problem.
>
> Bug: chromium:1467805
> Change-Id: Ie68a908842e3e45214f50eba396c67fed5e8bbd2
> Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/4728406
> Auto-Submit: Georg Neis <neis@chromium.org>
> Reviewed-by: Erik Chen <erikchen@chromium.org>
> Commit-Queue: Erik Chen <erikchen@chromium.org>
> Reviewed-by: Trent Apted <tapted@chromium.org>
> Cr-Commit-Position: refs/heads/main@{#1181829}

Bug: chromium:1467805
Change-Id: Id258ccb31cbbda0de990371b7bb029ad80db6f28
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/4776205
Reviewed-by: Erik Chen <erikchen@chromium.org>
Commit-Queue: Erik Chen <erikchen@chromium.org>
Auto-Submit: Georg Neis <neis@chromium.org>
Reviewed-by: Trent Apted <tapted@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1183008}