[sync] Simplify clearing of sync data in live tests

Before this patch, the internal state of SyncTest was temporarily
modified during SyncTest::ResetSyncForPrimaryAccount() to clear sync
data server-side (aka reset sync).

This complicated state override and reuse of SyncTest code can be
simplified because SyncServiceImplHarness offers most of the
functionality already, and there is also no need to turn
sync-the-feature on in order to clear data.

Change-Id: Id1a86f3ee88cfa1fc007ba346a7849af9e69be71
Bug: 40805441
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6624860
Reviewed-by: Rushan Suleymanov <rushans@google.com>
Commit-Queue: Mikel Astiz <mastiz@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1471754}