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Instead of each user of base setting the native-side global app context
separately, introduce a Java-side global app context, which is always
in sync with the native-side one. Switch most callers to setting
it on the Java side, except where this is problematic.

Callers of ApplicationStatus.getApplicationContext will be updated
incrementally in followup CLs once it's been verified that they only
require a Context and not a BaseChromiumApplication.

BUG=552419

Review URL: https://codereview.chromium.org/1407233017

Cr-Commit-Position: refs/heads/master@{#361306}