Fix bugs in docs

[gitttt-1234]

This PR makes several documentation fixes and improvements:

• Updates the docs workflow to use uv sync instead of pip.
• Fixes broken links on the inference page.
• Adjusts the menu order for better navigation.
• Add more instructions on how to use uvx.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 93.59%. Comparing base (ff91433) to head (08d3202).
⚠️ Report is 33 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #319      +/-   ##
==========================================
- Coverage   95.28%   93.59%   -1.70%     
==========================================
  Files          49       49              
  Lines        6765     6896     +131     
==========================================
+ Hits         6446     6454       +8     
- Misses        319      442     +123     

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