system-extensions: Dispatch start event after registration

Changes CrosWindowManagementContext from dispatching
`start` whenever CrosWindowManagement was created to
starting a Service Worker for the System Extension and then
dispatching the event.

This is in preparation for us starting service workers to
dispatch events.

Bug: b:242265231
Change-Id: I1532992648fd70f22831815ba8907f3d5bbb6dc9
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/3837453
Reviewed-by: Jiewei Qian <qjw@chromium.org>
Commit-Queue: Giovanni Ortuno Urquidi <ortuno@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1038569}