De-flake and re-enable a chrome.searchEnginesPrivate api test.

By checking the list of search engines, and only asserting against the one with
the expected name, we remove the dependency on order. This should get rid of
flakiness.

BUG=481924

Review URL: https://codereview.chromium.org/1121113002

Cr-Commit-Position: refs/heads/master@{#331060}