[Read aloud] Begin cleanup after pulling read aloud out of app.ts

This includes:
- Making private the methods that aren't used publicly
- Moving tests into VoicePackController test and out of more UI & app
  specific tests

Bug: 346612365
Change-Id: I77fb462bb1a8dab5c082d57b808d4b501a42bb41
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6534634
Commit-Queue: Lauren Winston <lwinston@google.com>
Auto-Submit: Kristi Saney <kristislee@google.com>
Reviewed-by: Lauren Winston <lwinston@google.com>
Cr-Commit-Position: refs/heads/main@{#1459064}