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That class doesn't really need to be ref-counted externally. There is one
catch: the caller is responsible for ensuring ClientCertStore is alive for the
duration of its async operation.

Resolve this by detaching it into a ref-counted Core internal to
SSLClientAuthHandler. Add a test to test this case.

Also make ContentBrowserClient's default client auth hook always select no
certificate so content_shell doesn't hang.

This relands the rest of https://codereview.chromium.org/596873002

BUG=439134

Review URL: https://codereview.chromium.org/795773002

Cr-Commit-Position: refs/heads/master@{#308142}