[blink scheduler] Remove IdleHelper::State

Instead, promote the state and methods to IdleHelper. This allows us to
remove some duplicated state (delegate_, helper_) and duplicated thread
checks (accessors were typically already behind thread checks). And
since only one instance of State was created (and afterwards updated),
this is a bit simpler and more readable.

Bug: 394906646
Change-Id: I6da9e57ee06d7deea6849e1787268bb030759dc2
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6250880
Commit-Queue: Scott Haseley <shaseley@chromium.org>
Reviewed-by: Stefan Zager <szager@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1422811}