Avoid late keyed services with TestingProfile

This patch migrates tests away from deprecated APIs and adopts
TestingProfile::Builder for tests in
/chrome/browser/android/webapps.

Rationale: creating or overriding keyed services after the profile has
been created is problematic and known to cause hard-to-debug test
flakiness, because it bypasses BrowserContextDependencyManager and often
leading to use-after-free.

This CL was uploaded by git cl split.

R=dominickn@chromium.org

Bug: 1106699
Change-Id: I7e4f896a89aefad57d56d41ed2e269995769e31a
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/2315155
Auto-Submit: Mikel Astiz <mastiz@chromium.org>
Reviewed-by: Dominick Ng <dominickn@chromium.org>
Commit-Queue: Mikel Astiz <mastiz@chromium.org>
Cr-Commit-Position: refs/heads/master@{#791557}