Reland "DLP: Improve file_manager integ tests"

This is a reland of commit 3647958307bd3503da66af9a7698689fa1b9a908

Original change's description:
> DLP: Improve file_manager integ tests
>
> Fixes some issues with the mocking in the files app DLP integration
> tests. The changes make the test code behave slightly closer to the
> actual code, but also reduce flakes and allow better assert statements.
>
> Bug: b/263079195
> Change-Id: If4b4170081bc13b0ff11ed1a08ba39e508011a71
> Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/4116716
> Reviewed-by: Aya Elsayed <ayaelattar@chromium.org>
> Commit-Queue: Aida Zolic <aidazolic@chromium.org>
> Cr-Commit-Position: refs/heads/main@{#1086702}

Bug: b/263079195
Change-Id: Ifbd62ddc33495e9c8d50cc2881746fdf1071c5a8
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/4124040
Auto-Submit: Aida Zolic <aidazolic@chromium.org>
Reviewed-by: Wenbo Jie <wenbojie@chromium.org>
Commit-Queue: Aida Zolic <aidazolic@chromium.org>
Reviewed-by: Aya Elsayed <ayaelattar@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1087279}