Clarify API contribution guides

[manwwe]

Update the API contribution documentation so it matches the current repository layout.

This PR:

• corrects outdated public and UI API route paths
• clarifies where generated OpenAPI specs are stored
• updates the endpoint contribution guide with current route/test locations
• fixes the Execution API versioning section so it reflects the current versions/ layout
• documents when to regenerate Task SDK models after Execution API schema changes

This is documentation-only. I validated the changed RST files with:

• prek run rst-backticks --files ...
• prek run blacken-docs --files ...
• git diff --check

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Was generative AI tooling used to co-author this PR?

• Yes — Codex

Generated-by: Codex following the guidelines

[boring-cyborg]

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