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.

client/src/pages/Workspace.tsx

@@ -70,12 +70,7 @@ import { useAiTools } from "../hooks/useAiTools";
 import { AiToolIcon } from "../components/AiToolIcon";
 import { LaneConsolePane } from "../components/run/LaneConsolePane";
 import PipelineMap from "../components/lanes/PipelineMap";
-import LaneCard, {
-  since,
-  LIVENESS_DOT,
-  LaneToolsMenu,
-  LaneRouterRow,
-} from "../components/lanes/LaneCard";
+import LaneCard, { since, LIVENESS_DOT, LaneToolsMenu } from "../components/lanes/LaneCard";
 import { AddLaneModal } from "../components/lanes/AddLaneModal";
 import { LaneChangesPanel } from "../components/lanes/LaneChangesPanel";
 import { WorkspaceHome } from "../components/lanes/WorkspaceHome";
@@ -883,8 +878,6 @@ export function Workspace() {
                     ))}
                   </select>
                 )}
-                {/* `agy` has no endpoint to point at a router. */}
-                <LaneRouterRow lane={currentLane} />
                 {/* No stage chip and no "auto: <stage>" chip here: the
                         PipelineMap right below this header already draws both
                         — the declared node as the current ring, the detected