[Sync] Make it impossible to get a reference to AndroidSyncSettings.
This change is motivated by some complex test flakiness issues that were
discovered in http://crrev.com/
1118833002. Making it impossible to store
a reference means that if we overwrite it for tests, we know everyone is
then using the overwritten version.
The approach here is to make every public method static and take the
context as an argument, so it can initialize the inner object if
necessary.
This CL is part 1/3 and leaves in deprecated versions of all the methods.
In part 2/3 the downstream uses of AndroidSyncSettings will be changed,
and in part 3/3 the deprecated methods will be removed upstream.
BUG=480604
Review URL: https://codereview.chromium.org/
1138013008
Cr-Commit-Position: refs/heads/master@{#330570}