[Extensions] Move delegated availability check map into extension client

This refactor shifts the repeated instances of getting feature
availability delegate information and passing it in when initializing
the extensions client, to instead happen inside extensions client
initialization itself.

No external behavior change is expected, although this does slightly
change the initialization of the extensions client inside the
ChromeUnitTestSuiteInitializer to actually use the real delegate instead
of one that always returns false for the controlled frame feature.

Bug: N/A
Change-Id: I14e1baa454af949be272b258620c752b90ad2e33
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5542807
Reviewed-by: Lei Zhang <thestig@chromium.org>
Reviewed-by: Devlin Cronin <rdevlin.cronin@chromium.org>
Commit-Queue: Tim <tjudkins@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1301675}