Discover registered Worktrees with generation-safe identity

[codeacme17]

Tracks #1.

Summary

Resolve the Current Project to its Git Repository and discover every registered Worktree with stable server-side identity and truthful actionable/unavailable state.

Scope

• Resolve a project anchor through Git commands to the canonical common Git directory.
• Treat git worktree list --porcelain -z as the sole authoritative Worktree inventory.
• Include Main and every valid linked Worktree regardless of path, Branch naming, creator, Codex registration, Detached HEAD, or custom root.
• Parse branch/detached commit, Main role, locked reason, prunable state, and canonical path without inspecting assumed .git/worktrees layouts.
• Produce opaque RepositoryId and generation-aware WorktreeId values from canonical Git identities.
• Represent missing/prunable registrations as unavailable diagnostics with no mutation capabilities.
• Rediscover a removed/restored/moved Worktree as fresh identity/state and never preserve cached Branch Occupancy across generations.
• Return a safe non-repository result for an ordinary directory.

Acceptance criteria

• A fixture containing Main, manual, Codex-style, Scheduled-style, Permanent-style, detached, custom-root, and unknown Worktrees shows every valid registration exactly once.
• Inclusion does not use path scans, .codex directories, Branch prefixes, or inferred provenance.
• Paths containing spaces, Unicode, leading dashes, and newlines parse correctly.
• Locked and prunable/missing states are distinct and neither is mislabeled as an active-operation lock.
• A removed and recreated Worktree at the same path invalidates its previous opaque IDs.
• A non-Git Current Project enables no Git mutation.

Out of scope

• Provenance labels, file status, Branch switching, Worktree lifecycle mutation, or automatic prune/repair.

Dependencies

• Bootstrap the TypeScript workspace and standalone runtime #3 and Implement the versioned loopback protocol and security boundary #5.

PRD coverage

• FR1; AC-01, AC-03, AC-04, and the identity portion of AC-22.

Verification

• Repository Engine contract tests against real temporary Git repositories and NUL-path parser fixtures.