(tooling): docs-sync pre-commit hook stages phantom src/content/docs/** paths when committing from a worktree

## Component

CDK / infrastructure — repo tooling (prek / pre-commit hooks)

## Describe the bug

The `docs-sync` pre-commit hook (`.pre-commit-config.yaml`) fails during a real `git commit` **from a linked git worktree** (`.worktrees//`, which `AGENTS.md` mandates for all feature work). The commit is blocked with:

```
sync docs → Starlight mirrors....Failed
- hook id: docs-sync
- files were modified by this hook
```

and `git status` fills with ~68 phantom `src/content/docs/**` entries staged at the **repo root** (`AD` — present in the index, absent on disk), e.g.:

```
AD src/content/docs/architecture/Api-contract.md
AD src/content/docs/index.md
AD src/content/docs/using/Jira-setup-guide.md
... (~68 total)
```

The real Starlight mirror under `docs/src/content/docs/` is regenerated **correctly** — only these root-relative phantom paths are spurious, and they block the commit.

## Expected behavior

Committing an edit to a file matching the hook's `files:` pattern (`docs/(design|guides)/*.md` or `CONTRIBUTING.md`) from a worktree regenerates the mirror, stages only the real `docs/src/content/docs/**` files, and the hook passes.

## Current behavior

- **Reproduces only on a real `git commit`** from a worktree — not via `prek run docs-sync ...` (which passes cleanly). This points at prek's commit-time behavior (it stashes unstaged changes during the run), not the sync script itself.
- The hook entry is:
```yaml
entry: bash -lc 'cd "$(git rev-parse --show-toplevel)/docs" && node scripts/sync-starlight.mjs && git add src/content/docs/'
```
In a worktree, `git rev-parse --show-toplevel` correctly returns the worktree root, and `sync-starlight.mjs` resolves its output to `docs/src/content/docs/` correctly. Running the entry line **manually** stages the right path. Yet under a real commit, ~68 root-relative `src/content/docs/**` paths end up `AD` in the index.
- Workaround: `git reset`, explicitly stage the intended files, and commit with `--no-verify` (after verifying the mirror out-of-band with `mise //docs:sync`).

## Reproduction steps

1. `git worktree add .worktrees/docs-fix -b docs/test origin/main`
2. `cd .worktrees/docs-fix && mise run install`
3. Append a line to `docs/guides/LINEAR_SETUP_GUIDE.md` and `git add` it.
4. `git commit -m "docs: test"` (run through `mise exec --` so the `astro check` hook gets Node 22 — see the related Node-version issue).
5. Observe: `docs-sync` reports **Failed — "files were modified by this hook"**, and `git status` shows ~68 phantom `AD src/content/docs/**` entries at the repo root while the real mirror under `docs/src/content/docs/` is correct.

Note: `prek run docs-sync --files docs/guides/LINEAR_SETUP_GUIDE.md` does **not** reproduce it — the failure is specific to the full commit path.

## Possible solution

Not root-caused with confidence; the trigger is the commit-time path (prek stash + the hook's `git add`), not the sync script. Candidate directions to investigate:

- Make the hook's `git add` target explicit and worktree/cwd-independent so it cannot resolve against an unexpected root during prek's stash/restore, e.g. `git -C "$(git rev-parse --show-toplevel)" add docs/src/content/docs/`.
- Confirm whether prek's partial-stash step interacts badly with a hook that both writes files and stages them, in a worktree specifically.

## Node version

22.23.1 (via mise)

## mise version

2026.7.13

## Local modifications

Discovered while committing an unrelated CLI fix from a worktree at `.worktrees/`. No changes to the hook itself; the symptom is independent of the committed content.

## Additional context

`AGENTS.md` requires all feature work in a worktree under `.worktrees//`, so this affects the mandated workflow for any change touching `docs/guides/`, `docs/design/`, or `CONTRIBUTING.md`. Related issue: `astro check` hook fails under bare Node v20 unless the commit runs through `mise exec` (filed separately).

Start with the docs-sync entry in .pre-commit-config.yaml and scripts/sync-starlight.mjs, then reproduce the real commit from a linked worktree rather than using prek run directly. Inspect how prek's commit-time stash interacts with the hook's git add and repository root. Done means a worktree commit stages only docs/src/content/docs/**, passes the hook, and leaves no root-relative phantom paths.

Written by the indexing model from the issue text.