[sync] Fix flaky MoveThemePrefsToSpecifics sync test

This fixes the flakiness in
SingleClientThemesWithMoveThemePrefsToSpecficsiEnabledSyncTest.ShouldNotApplyThemeFromSyncingPrefsIfFlagMarked
by waiting for the prefs in the PRE_ test to commit to disk before exit.

Fixed: 388236931
Change-Id: I8965549c7af09549642d92feaaaaa2a91d4fc2df
Cq-Include-Trybots: luci.chromium.try:linux_chromium_msan_rel_ng,mac14-arm64-rel,mac_chromium_asan_rel_ng
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6162855
Code-Coverage: findit-for-me@appspot.gserviceaccount.com <findit-for-me@appspot.gserviceaccount.com>
Auto-Submit: Ankush Singh <ankushkush@google.com>
Reviewed-by: Rushan Suleymanov <rushans@google.com>
Commit-Queue: Rushan Suleymanov <rushans@google.com>
Cr-Commit-Position: refs/heads/main@{#1404113}