Fix syncing of branch node executions and add integration test

[Sovietaced]

Tracking issue

Closes: flyteorg/flyte#6490

Why are the changes needed?

Fixes an issue where flyte remote breaks

What changes were proposed in this pull request?

Move fix from 6a4c2d8 around and add integration test to validate it.

How was this patch tested?

Added an integration test

Setup process

Screenshots

Check all the applicable boxes

• I updated the documentation accordingly.
• All new and existing tests passed.
• All commits are signed-off.

Related PRs

Docs link

[codecov]

Codecov Report

❌ Patch coverage is 0% with 16 lines in your changes missing coverage. Please review.
✅ Project coverage is 79.34%. Comparing base (8d4b122) to head (bbb855b).
⚠️ Report is 1 commits behind head on master.

Files with missing lines	Patch %	Lines
flytekit/remote/remote.py	0.00%	16 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #3372      +/-   ##
==========================================
- Coverage   83.58%   79.34%   -4.25%     
==========================================
  Files           3      216     +213     
  Lines         195    22734   +22539     
  Branches        0     2986    +2986     
==========================================
+ Hits          163    18038   +17875     
- Misses         32     3865    +3833     
- Partials        0      831     +831     

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