fix: rewrite staggered_race to be race safe

[bdraco]

What do these changes do?

We keep using stdlib asyncio.staggered.staggered_race and we keep having issues with it

While I hate to maintain our own, it seems like we need to do this

Are there changes in behavior for the user?

bugfix

Related issue number

fixes #100
fixes #99
fixes #96
#93 - maybe related, unknown
#97 - this looks like a deeper problem
aio-libs/aiohttp#8599 - this is what the new implementation from stdlib was intended to solve but it has other regressions

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 100.00%. Comparing base (b075f25) to head (9fd0030).
Report is 2 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff            @@
##              main      #101   +/-   ##
=========================================
  Coverage   100.00%   100.00%           
=========================================
  Files            6         5    -1     
  Lines          198       227   +29     
  Branches        45        60   +15     
=========================================
+ Hits           198       227   +29     

Flag	Coverage Δ
	99.55% <100.00%> (+0.56%)	⬆️

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