Have a list of fall-back engines to try for private window search

[bsclifton]

Fixes brave/brave-browser#6421

Problem was regular DDG not found in the entries returned (since locale specific was returned instead).

Besides adding other entries, this also puts a dcheck in place to ensure an engine gets set (otherwise, the error thrown is no immediately clear and a bit hard to trace).

(bug unintentionally introduced with #3591)

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Test Plan:

See brave/brave-browser#6421

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After-merge Checklist:

• The associated issue milestone is set to the smallest version that the
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[simonhong]

LGTM. Using do-while or range for-loop depends on your preference :)

[bsclifton]

Lint has failures which are unrelated to this PR - but otherwise, looks good!