Dictation: Remove SuccessWaiter class

We are trying to remove all polling from Dictation tests, so this
change removes the SuccessWaiter class. Instead of polling for the
commit text, we modify the MockImeInputContextHandler to notify
observers whenever the commit text is updated. This allows us to
swap out a polling-based approach for an event-based approach.

CQ_INCLUDE_TRYBOTS=luci.chrome.try:chromeos-betty-pi-arc-chrome

AX-Relnotes: N/A
Bug: b:264535324
Change-Id: I03e2dc6c870c90fac621048c1e67810e3edf678f
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/4195041
Reviewed-by: Darren Shen <shend@chromium.org>
Commit-Queue: Akihiro Ota <akihiroota@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1097761}