feat(python): Drop nest-asyncio in favor of custom logic

[stinodego]

In Polars Cloud we implemented this nested async functionality without a dependency. Figured we should do the same for the open source repo.

[codecov]

Codecov Report

Attention: Patch coverage is 80.95238% with 4 lines in your changes missing coverage. Please review.

Project coverage is 79.77%. Comparing base (87b03aa) to head (80805f5).
Report is 6 commits behind head on main.

Files with missing lines	Patch %	Lines
py-polars/polars/io/database/_utils.py	80.95%	2 Missing and 2 partials ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main   #20793      +/-   ##
==========================================
- Coverage   79.78%   79.77%   -0.01%     
==========================================
  Files        1561     1561              
  Lines      222001   222014      +13     
  Branches     2531     2533       +2     
==========================================
+ Hits       177117   177121       +4     
- Misses      44302    44309       +7     
- Partials      582      584       +2     

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[ritchie46]

Nice one!