Migrate GetListDeprecated() calls in media/.

Also update some of the surrounding code to use non-deprecated
base::Value APIs, as it's a bit cleaner not to mix the deprecated and
non-deprecated base::Value APIs.

Bug: 1338341
Change-Id: I6cecfe904773c31a947af243685014c82a806f6f
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/4051369


Commit-Queue: Matt Menke <mmenke@chromium.org>
Reviewed-by: Thomas Guilbert <tguilbert@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1076493}