[ci] [doc] automation after migrating to uv

[vkarak]

Also:

• Add note about uv bug mishandling marker-based default dependencies.
• The deploy.sh script was renamed to make_release.sh as it's a more accurate name.

Closes #3693.
Closes #3692.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 91.92%. Comparing base (f0df59f) to head (d0c6ca9).

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #3715      +/-   ##
==========================================
+ Coverage   91.91%   91.92%   +0.01%     
==========================================
  Files          62       62              
  Lines       13783    13783              
==========================================
+ Hits        12668    12670       +2     
+ Misses       1115     1113       -2     

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