[Sync] Consolidate DataTypeController methods that post on the backend thread

tools/heapcheck/suppressions.txt

 # There are three kinds of suppressions in this file.
 # 1. third party stuff we have no control over
 #
 # 2. intentional unit test errors, or stuff that is somehow a false positive
 # in our own code, or stuff that is so trivial it's not worth fixing
 #
 # 3. Suppressions for real chromium bugs that are not yet fixed.
 # These should all be in chromium's bug tracking system (but a few aren't yet).
 # Periodically we should sweep this file and the bug tracker clean by
 # running overnight and removing outdated bugs/suppressions.
@@ skipping 1708 matching lines @@
    Heapcheck:Leak
    fun:WTF::fastMalloc
    fun:WTF::StringImpl::createUninitialized
    fun:WTF::String::fromUTF8
    ...
    fun:WebKit::WebString::fromUTF8
    ...
    fun:PeerConnectionHandlerTest_Basic_Test::TestBody
 }
 {
-   bug_105667_a
-   Heapcheck:Leak
-   fun:browser_sync::TypedUrlDataTypeController::StartAssociationAsync
-   fun:browser_sync::NonFrontendDataTypeController::Start
-   fun:browser_sync::DataTypeManagerImpl::StartNextType
-   fun:browser_sync::DataTypeManagerImpl::DownloadReady
-}
-{
-   bug_105667_b
-   Heapcheck:Leak
-   fun:browser_sync::TypedUrlDataTypeController::StopAssociationAsync
-   fun:browser_sync::NonFrontendDataTypeController::Stop
-   fun:browser_sync::DataTypeManagerImpl::FinishStop
-   fun:browser_sync::DataTypeManagerImpl::Stop
-   ...
-   fun:ProfileSyncService::Shutdown
-}
-{
    bug_108398
    Heapcheck:Leak
    ...
    fun:BrowserThemePack::BuildFromExtension
    fun:BrowserThemePackTest_CanBuildAndReadPack_Test::TestBody
 }
 {
    bug_108399
    Heapcheck:Leak
    ...
@@ skipping 72 matching lines @@
    fun:v8::internal::NativeObjectsExplorer::IterateAndExtractReferences
    fun:v8::internal::HeapSnapshotGenerator::CountEntriesAndReferences
    fun:v8::internal::HeapSnapshotGenerator::GenerateSnapshot
    fun:v8::internal::HeapProfiler::TakeSnapshotImpl
    fun:v8::internal::HeapProfiler::TakeSnapshotImpl
    fun:v8::internal::HeapProfiler::TakeSnapshot
    fun:v8::HeapProfiler::TakeSnapshot
    fun:GetNumObjects
    ...
 }