[IntentHandling] Launch file_browser_handlers in App Service (ash)

Redirect the launching of extensions through App Service, in ash
only. The launch process for extensions is quite different to
Chrome apps.

This CL re-uses the existing implementation for actually doing
all of the extension-specific launch behaviour, which is in
ExecuteFileBrowserHandler(). We just do it through App service
so that both Ash and Lacros go through App service.

Cq-Include-Trybots: luci.chrome.try:linux-chromeos-chrome
Bug: 1240018
Change-Id: I5a498916f6c594992416a986990553fc2492201c
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/3301359
Commit-Queue: Peter Marshall <petermarshall@chromium.org>
Reviewed-by: Maggie Cai <mxcai@chromium.org>
Reviewed-by: Alex Danilo <adanilo@chromium.org>
Cr-Commit-Position: refs/heads/main@{#945853}