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/components/lanes/WorkspaceRowMenu.tsx

@@ -2,8 +2,7 @@
  * @file WorkspaceRowMenu — the sidebar workspace row's context menu, opened at
  * the pointer (right-click) or under the row's `⋯` button. Every item is an
  * existing call: Start/Stop (`POST /api/lanes/:id/start` slot 0 / `stop`),
- * Rename (the row's inline field), the AI Router select (`LaneRouterRow`,
- * router-capable tools only), Create/update readme (claude only, the same run
+ * Rename (the row's inline field), Create/update readme (claude only, the same run
  * the lane Tools menu starts), New workspace here (the Add modal prefilled),
  * Copy path, and Reset/Remove through `DestructiveLaneModal` — Reset only on a
  * managed lane. The server's guards are the real ones; the menu only hides
@@ -16,7 +15,6 @@ import { useEffect, useRef, useState } from "react";
 import { useTranslation } from "react-i18next";
 import { api } from "../../lib/api";
 import type { Lane } from "../../lib/types";
-import { LaneRouterRow } from "./LaneCard";
 
 export type WorkspaceMenuAction = "rename" | "new-here" | "reset" | "remove" | "started";
 
@@ -93,9 +91,6 @@ export function WorkspaceRowMenu({
       <button type="button" role="menuitem" className={item} onClick={() => onAction("rename")}>
         {t("menu.rename")}
       </button>
-      <div className="px-2 py-1">
-        <LaneRouterRow lane={lane} />
-      </div>
       {lane.tool === "claude" && (
         <button
           type="button"