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/LANES.md

@@ -87,7 +87,7 @@ terminal with `agenthub lanes add --pipeline <id>`. *Model endpoint* is the one
 per-workspace extra the form still asks for, and it sits in the form itself rather
 than behind a disclosure — a disclosure around a single field only hid it.
 
-The **Model endpoint** radio chooses between **Native** (the vendor's own API) and **AI Router** — a profile saved in Settings › AI Router (9Router, OpenRouter, a self-hosted gateway). Choosing one writes it into the new workspace's own config as the workspace is created: a claude workspace gets the `env` block of its `.claude/settings.local.json`, a codex workspace gets a `$CODEX_HOME/<name>.config.toml` layer plus a `-p <name>` on every spawn. With no profile saved the radio stays on Native and says so. Unlike the workspace's tool, this one is not immutable: an existing workspace's detail header in Workspace carries a **Model** select (beside the pipeline picker) showing its current profile, and picking another calls `POST /api/lanes/:id/router/apply`, rewriting the workspace's config and its `router_profile` column together. (The select is hidden when `native` is the only profile — there would be nothing to choose.) A failed apply puts the select back rather than leaving the row claiming a router the workspace did not get, and marks itself `⚠` with the error in its tooltip. A session already running in the pane is only HALF switched: Claude Code re-applies an `env` block to a live session when the file changes, but the session's model was resolved at startup, so the previous router's model name keeps being sent to the new endpoint and the next prompt fails with a model-not-found error (switching back to Native included). The route therefore answers `restart_required: true` plus the `run_id` whenever a pane is live, and the select renders a **Restart** button that kills that pane and opens a fresh one — started from the workspace id alone, since replaying the old run's `--model` would re-create the same mismatch. Editing or deleting the profile itself in Settings also reaches every workspace using it: an edit re-applies it (so a rotated key actually lands), a delete resets those workspaces to Native. See `docs/API.md` § AI Router profiles.
+A workspace has no AI Router of its own: each NEW session picks one. The **AI Router** select beside the model picker — in the workspace home's prompt box and in a pane's run form — lists the profiles saved in Settings › AI Router (9Router, OpenRouter, a self-hosted gateway) plus **Native** (the vendor's own API); it is hidden when only Native exists or the workspace's tool cannot use a router (only Claude and Codex can), and it remembers the last pick (`agenthub.session.router`). The start sends `router: "<name>"`; a Claude pane then runs with `--settings=<data dir>/router-settings/<name>.json`, which outranks the workspace's own settings, and a Codex pane with `-p <name>` plus its key through tmux `-e`. So two sessions of one workspace can run on two routers, a worktree session gets its router too, and switching never touches a running session. A resume goes back to the router its session last ran on (`dashboard_runs.router`). Editing a profile in Settings rewrites those files (a rotated key reaches live Claude sessions); deleting it removes them. Older builds wrote a workspace's router into its `.claude/settings.local.json`; every server start takes those eight keys back out. See `docs/API.md` § AI Router profiles.
 
 Both modes' path field has a **Browse** button next to it, opening a small folder browser (`GET /api/lanes/browse?path=<abs>`) instead of a native OS picker — a browser cannot hand a web page an absolute filesystem path from a native dialog, so this dashboard (local-first, server and browser on the same machine) lists directories server-side instead: click a subfolder to descend, ".." to go up, "Select this folder" to fill the path field. Git repos are marked in the listing.