Standardize README, PyPI, and docs-site badge surfaces

[cmccomb]

Summary

Standardize the badge/shield surfaces in design-research-problems across the GitHub README, the PyPI-rendered README, and the Sphinx docs landing page.

Current state

• The README already has a relatively rich badge set.
• The docs landing page does not currently expose a matching badge row.
• The repo should align with the same badge baseline as the other module repos while the docs shell and catalog work are being redesigned.

Proposed work

• Adopt the shared badge baseline across module repos.
• Keep or refine the existing README badges so they match that standard.
• Add a consistent badge/shield section to the docs landing page.
• Verify the final badge approach renders cleanly in GitHub README and PyPI.

Acceptance criteria

• The README and docs landing page use the same shared badge baseline.
• Badge markup is safe for GitHub + PyPI rendering.
• The badge treatment complements the new user-facing catalog work rather than competing with it.