Documentation missing for GH_AW_GITHUB_TOKEN magic secret

Alright, this is me the human writing this paragraph. I think there was a documentation regression in #17990 that caused me a lot of pain over the last couple hours. I'll leave the opus-generated summary below (and I did read it and think it covers it pretty well). I just don't like posting pure GenAI issues without a human-authored frontmatter at this point.

**Summary**

Recent documentation refactoring (especially PR #17990) has removed specific guidance about the `GH_AW_GITHUB_TOKEN` magic secret. Users are left without clear instructions about:
- When and why `GH_AW_GITHUB_TOKEN` is required (especially for tools.github in lockdown mode, safe outputs writing content, etc.)
- What permissions are needed for the PAT used as this secret
- How to create the token for both individual and organization-owned repos
- How it interacts with the fallback chain `${{ secrets.GH_AW_GITHUB_TOKEN || secrets.GITHUB_TOKEN }}`

**Context / Impact**
- Workflows compiled by `add-wizard` and others routinely reference `${{ secrets.GH_AW_GITHUB_TOKEN || secrets.GITHUB_TOKEN }}`, but the only documentation left are scattered code comments and snippets in lockdown-mode.md, with no coherent, full description.
- This leaves new users confused about requirements for agentic workflows that WRITE to issues/discussions, especially in public repos with lockdown mode enabled.
- Previous docs in `auth.mdx` provided detailed guidance; that section was deleted and not fully reincorporated into new dedicated pages.

**Recommendation**
- Restore comprehensive documentation for `GH_AW_GITHUB_TOKEN`.
- Include:
- Clear description of WHEN it's required
- Step-by-step PAT creation instructions (with links to GitHub's PAT UI)
- Explicit list of required scopes/permissions for agentic workflows
- Notes on public vs. private repos, lockdown mode, and fallback logic
- References to relevant YAML snippets/code to make requirements obvious
- Ideally, the docs should live in `auth-projects.mdx`, `github-tools.md`, or a new dedicated page (as appropriate).

**Related files / evidence**
- [Current auth.mdx](https://github.com/github/gh-aw/blob/main/docs/src/content/docs/reference/auth.mdx) — no mention of `GH_AW_GITHUB_TOKEN`
- [lockdown-mode.md](https://github.com/github/gh-aw/blob/main/docs/src/content/docs/reference/lockdown-mode.md) — only brief examples referencing the secret
- PR #17990 — removed old auth guidance
- Compiled workflow YAML routinely references this secret

**Tactful ask:**
Could maintainers please add back clear documentation for `GH_AW_GITHUB_TOKEN` and its requirements so new and existing users can correctly configure authentication for writing agentic workflows?