feat: AI Router per session; Settings at the sidebar's foot; shipped tool icons

AI Router is a session's choice, not a workspace's:
- an AI Router select beside the model picker in the workspace home and a
  pane's run form (RouterPicker.tsx; hidden off Claude/Codex or with only
  Native; last pick remembered in agenthub.session.router)
- `router` on POST /api/lanes/:id/start and POST /api/run; Claude gets
  --settings=<data dir>/router-settings/<name>.json (0600, outranks project
  and user settings, key never in argv), Codex -p <name> + key via tmux -e
- dashboard_runs.router; a resume naming none goes back to it
- profile PATCH rewrites the session files, DELETE removes them
- gone: POST /api/lanes/:id/router/apply, LaneRouterRow, the Add-workspace
  router radio, the claude-/codex-home `routers` answers; clearLaneRouters
  takes the old keys out of each workspace's settings.local.json at start

Sidebar: Settings pinned to the foot, the collapse toggle beside it (stacked
on the rail) instead of in the brand's corner.

Icons: shipped SVG marks for claude, codex, openclaw and hermes (a
black/white pair swapped by theme) in client/public/ai-tools/, used by
AiToolIcon before the server's favicon.

docs/plans/desktop-parity/README.md

@@ -50,7 +50,7 @@ archived, and give a session — not a project — its own worktree.
 | 3 | Drop the activity bar's **Sessions** tab (third copy of the same list) | small |
 | 4 | **Fork** a Claude session into a free pane (`--resume <id> --fork-session`) | small |
 | 5 | Ctrl/Cmd+click a live session in the sidebar opens it in a second pane | small |
-| 6 | Worktree per session = child workspace (D4) — **ask first** | large |
+| 6 | Worktree per session, Claude's way (D4) | large |
 | 7 | Comment on a diff line → text pasted into the session's prompt | medium, optional |
 
 ### Phase 1 — session ownership