[docs] Add contributor guide for editing and managing Python dependencies

[ans9868]

Summary

Adds a contributor guide for editing and managing Ray's Python dependencies. Covers the three-layer architecture (source files → compiled requirements → per-image lock files), how to add or update a dependency, how to diagnose conflicts with uv vs pip, and the edge cases that bite contributors (ARM64 skip, platform-specific CPU vs GPU wheels, Wanda Docker cache invalidation, requirements.txt ↔ setup.py sync requirement).

Why

Completes item 4 of #60512. I had to map out the dependency structure and hit most of the gotchas described here while landing #60522 (modernizing AxSearch for ax-platform 1.0+). This doc is meant to keep the next contributor out of those holes.

Scope

Two files, pure docs change. No build-system changes, no lock regeneration needed.

• doc/source/ray-contribute/dependency-management.md (new)
• doc/source/ray-contribute/getting-involved.rst (one-line toctree entry)

The page slots into the Getting Involved / Contributing sidebar between "CI Testing Workflow on PRs" and "Contributing to the Ray Documentation."

Built locally with make develop under -W (warnings-as-errors). There are no Sphinx warnings on the new file.

Miscellaneous

The framing of this doc borrows from @elliot-barn's ray-dependencies skill on the elliot-barn-dependencies-skill branch, especially the requirements.txt ↔ setup.py sync rule.

@aslonnie / @elliot-barn -- you were both deep in the dependency issues during #60522 (and the related side-quest PRs I opened along the way, #62596 and #62471). Happy to have either of you review if you have time.

[gemini-code-assist]

Code Review

This pull request introduces a new documentation guide, dependency-management.md, which provides a comprehensive overview of Ray's three-layer Python dependency structure (Source, Compiled, and Locks). It also includes instructions for updating dependencies and troubleshooting resolution conflicts using tools like uv. The review feedback identifies minor typographical errors, trailing whitespace, and capitalization inconsistencies for terms like 'Python', 'Ray', and 'uv'.