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This CL is not expected to address the test flakiness issue but it
is cleaning the test code a bit for style and functional issues.

The following has been done:
- renamed the file to .cc so that it can be linted
- moved the type aliases into an anonymous namespace and used ::
because we aliased names in namespaces we did not own.
- replaced a static base::FilePath
- used the test server handle to guarantee the shutdown of
the test server, as suggested by the documentation
- cleaned up the request handler
- inlined some local variables
- removed a UT for creating the fetcher, since that code was
already tried in other tests.

Bug: 1153304
Change-Id: I01ef5d21ea354a6fcc7a08d0acd1e744f19e816c
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/2575383
Commit-Queue: Sorin Jianu <sorin@chromium.org>
Reviewed-by: Joshua Pawlicki <waffles@chromium.org>
Cr-Commit-Position: refs/heads/master@{#833895}