Fix issue that sync callback is started twice

[bitfriend]

I found that sync callback is started twice.
This affects the initial loading time and probably may occur app crash due to too frequent mutex locks.

[bitfriend]

The following screenshot shows that sync callback is started twice.

[codecov]

Codecov Report

Attention: Patch coverage is 0% with 10 lines in your changes missing coverage. Please review.

Project coverage is 33.31%. Comparing base (e0c1c79) to head (f1621cf).

Files with missing lines	Patch %	Lines
.../lib/common/providers/notifiers/sync_notifier.dart	0.00%	10 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #2642      +/-   ##
==========================================
- Coverage   33.35%   33.31%   -0.05%     
==========================================
  Files         744      744              
  Lines       48314    48320       +6     
==========================================
- Hits        16116    16096      -20     
- Misses      32198    32224      +26     

Flag	Coverage Δ
integration-test	43.30% <ø> (-0.11%)	⬇️
unittest	24.11% <0.00%> (-0.01%)	⬇️

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[bitfriend]

This screenshot shows that alwaysClientProvider callback is called twice.

[bitfriend]

alwaysClientProvider is based on AlwaysClientNotifier that is listening to clientProvider.
As a result, alwaysClientProvider is the wrapper of clientProvider.
So that callback seems to be called twice.

[bitfriend]

When SyncNotifier listens to clientProvider instead of alwaysClientProvider, sync callback is started only once.

[bitfriend]

I recall alwaysClientProvider was used here to avoid that guest client (not-logged-in) starts sync callback.