docs: Revamp documentation with pydata theme

[borchero]

Motivation

It all started with trying to fix the current warnings in the docs. Turns out that many links in the API docs were broken and the design generally didn't help readability. Hence, this PR just refactors the entire thing.

Changes

• Use the pydata sphinx theme and take plenty of inspiration from the polars docs setup
• Manually structure the entire API documentation, introducing semantic grouping of methods
• Remove all warnings and make doc builds fail on warnings
• Ensure that pixi run docs always runs a clean build

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 100.00%. Comparing base (91961d5) to head (c91c525).
⚠️ Report is 1 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff            @@
##              main      #200   +/-   ##
=========================================
  Coverage   100.00%   100.00%           
=========================================
  Files           53        53           
  Lines         2996      2996           
=========================================
  Hits          2996      2996           

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[borchero]

Rendered docs: https://dataframely--200.org.readthedocs.build/200/