Downloads WebUI: Convert SearchServiceUnitTest to browser_tests.

This is in preparation of migrating to Polymer3. JS unit tests (V8UnitTest)
have no way currently of loading JS modules within a test context, since
they rely on a chrome://test data source that only exists in a
browser_tests context (WebUIBrowserTest).

Bug: 1022215
Change-Id: Ieb8caa155d3b83567160eb0927f43adbf548b153
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/1918650
Auto-Submit: Demetrios Papadopoulos <dpapad@chromium.org>
Reviewed-by: Rebekah Potter <rbpotter@chromium.org>
Commit-Queue: Demetrios Papadopoulos <dpapad@chromium.org>
Cr-Commit-Position: refs/heads/master@{#715582}