[client] Fix race condition in Metadata.Get

[TylerHelmuth]

Description:
Fixes a bug where Get was not thread safe.

Link to tracking Issue:
Closes #9594

Testing:
Tested locally

[dmitryax]

@TylerHelmuth PTAL at the failing tests

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Comparison is base (df96393) 90.69% compared to head (0576a00) 90.70%.
Report is 1 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #9595      +/-   ##
==========================================
+ Coverage   90.69%   90.70%   +0.01%     
==========================================
  Files         347      347              
  Lines       18211    18210       -1     
==========================================
+ Hits        16516    16518       +2     
+ Misses       1371     1369       -2     
+ Partials      324      323       -1     

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[TylerHelmuth]

@jpkrohling please also take a look.