Revert "[Android] Remove sync from PasswordGenerationIntegrationTest"

This reverts commit adef9255366094caf9092b863cb3b465721676b8.

Reason for revert: Suspected causing test failures on Android bots. See crbug.com/386203782 for more details.

Original change's description:
> [Android] Remove sync from PasswordGenerationIntegrationTest
>
> Bug: 41493794
> Change-Id: I109a200e518f3dfdcd369d9919531d7d9df0ae45
> Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6109038
> Commit-Queue: Boris Sazonov <bsazonov@chromium.org>
> Auto-Submit: Tanmoy Mollik <triploblastic@google.com>
> Reviewed-by: Boris Sazonov <bsazonov@chromium.org>
> Cr-Commit-Position: refs/heads/main@{#1400260}

Bug: 41493794
Change-Id: I37c179b678fb930c373289800a6d9ecce4142a16
No-Presubmit: true
No-Tree-Checks: true
No-Try: true
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6114640
Bot-Commit: Rubber Stamper <rubber-stamper@appspot.gserviceaccount.com>
Commit-Queue: Hailey Wang <haileywang@google.com>
Auto-Submit: Hailey Wang <haileywang@google.com>
Owners-Override: Hailey Wang <haileywang@google.com>
Cr-Commit-Position: refs/heads/main@{#1400306}