Reland "[Files]: Run unit test with V1 version of search."

This is a reland of commit cfeaa9b6
It got reverted though there is no evidence that it was the cause of failure of another test.

Original change's description:
> [Files]: Run unit test with V1 version of search.
>
> The unit test as it is currently written, works with V1 version only.
> This small CL just makes it so that the test will not start failing
> after we enable search V2 by default.
>
> Bug: b:241868453
> Change-Id: Ib45791c65b149f120e52a466928249140eaaf2a5
> Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/4551400


> Commit-Queue: Bo Majewski <majewski@chromium.org>
> Reviewed-by: Luciano Pacheco <lucmult@chromium.org>
> Cr-Commit-Position: refs/heads/main@{#1147597}

Bug: b:241868453
Change-Id: Ie796ec6f5af46ebda6b0ceb06364b1edd9a4333b
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/4554539


Commit-Queue: Bo Majewski <majewski@chromium.org>
Reviewed-by: Luciano Pacheco <lucmult@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1148345}