What changed

• propagate workspace linked directories into slash-command discovery and cache keys so command lists refresh when /add-dir changes
• prepend linked-directory context to Claude prompts using the shared helper, and pass linked directories through Claude slash-command listing with the required env flag
• invalidate the frontend slash-command query when linked directories change and add coverage for the new request parsing and sidecar behavior

Why

Previously slash-command results could stay stale after linked directories changed, and Claude handled linked-directory context differently from Codex. This makes linked directories affect command discovery consistently and keeps the UI in sync.

Follow-up / test notes

• pre-commit hooks passed during commit: biome check --write, cargo fmt, cargo clippy -- -D warnings
• I did not run the full test suite separately before opening this PR