PR summary

Towards #30877.

This documents how to install matplotlib using uv. Additionally, it consolidates and tests all documented build paths in a new action. I've omitted adding uv.lock for now.

Pixi is handled in #31384, though note that uv is easier since it needs no additional configuration to work out of the box.

This does add 12 build smoke tests over 3 actions, which may be overkill. I'm open to thoughts on how many of these are really needed, but the ubuntu conda failure is surfacing the real issue in #30961 so I'm inclined to say these are worth keeping.

AI Disclosure

Claude code took a first pass, manually touched up and rewrote the docs.

PR checklist

• [n/a] "closes #0000" is in the body of the PR description to link the related issue
• new and changed code is tested
• [n/a] Plotting related features are demonstrated in an example
• [n/a] New Features and API Changes are noted with a directive and release note
• Documentation complies with general and docstring guidelines