[Promise Icons] Add PromiseAppRegistryCache Observer class

Create PromiseAppRegistryCache::Observer class and update the
PromiseAppService unit test class to become an observer. This allows us
to wait for registry cache updates instead of using RunUntilIdle().

Bug: b/261907495
Change-Id: Ie8e680a53e2d5a9cc366b7d08beb2fdae23dbfcb
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/4549037


Reviewed-by: Maggie Cai <mxcai@chromium.org>
Commit-Queue: Vivian Pao <vpao@google.com>
Cr-Commit-Position: refs/heads/main@{#1148912}