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/i18n/locales/en/lanes.json

@@ -40,23 +40,15 @@
   "addLaneRepoHintAdopt": "An existing directory. The dashboard tracks it as-is — no worktree, no new branch.",
   "addLaneRepoLabel": "Source repository",
   "addLaneRepoLabelAdopt": "Directory",
-  "addLaneRouterCustom": "AI Router",
-  "addLaneRouterEmptyHint": "No router profile saved yet — add one under Settings › AI Router.",
-  "addLaneRouterHint": "Native talks to the vendor's own API. An AI Router profile is written into this workspace's own config when it is created.",
-  "addLaneRouterLabel": "Model endpoint",
-  "addLaneRouterLoading": "Loading router profiles…",
-  "addLaneRouterProfileLabel": "Router profile",
   "addLaneSetupClose": "Close",
   "addLaneSetupMcp": "MCP servers",
   "addLaneSetupProfile": "Profile",
-  "addLaneSetupRouter": "Model endpoint",
   "addLaneSetupTitle": "Setup",
   "addLaneTitleLabel": "Title",
   "addLaneTitlePlaceholder": "Optional",
   "addLaneToolDefaultBadge": "Default",
   "addLaneNoTools": "No AI tool is installed and enabled.",
   "addLaneNoToolsLink": "Open Settings → AI Tools",
-  "addLaneRouterNativeTool": "Native ({{tool}})",
   "addLaneToolHint": "Which CLI drives this workspace. Cannot be changed later.",
   "addLaneWorktreeDetached": "(detached)",
   "addLaneWorktreesMore": "+{{count}} more",
@@ -222,13 +214,8 @@
   "proof.ticketReport": "Task report",
   "renameLabel": "Rename this workspace",
   "reorderHint": "Drag to reorder · Alt+←/→",
-  "router.applied": "Applied.",
   "router.native": "Native ({{tool}})",
-  "router.nativeOnly": "{{tool}} runs on its own settings — AI Router profiles work with Claude Code and Codex only.",
-  "router.appliedRestart": "Applied, but the session running in this workspace still uses the old models — restart it to take effect.",
-  "router.label": "Model",
-  "router.restart": "Restart",
-  "router.restarted": "Session restarted with the new router.",
+  "router.label": "AI Router",
   "runtime.boot": "▶ up",
   "runtime.busy.down": "stopping…",
   "runtime.busy.up": "booting…",

client/src/i18n/locales/en/settings.json

@@ -67,8 +67,7 @@
   "claudeHome": {
     "title": "CLAUDE_HOME",
     "description": "Root directory for Claude Code session data. Changing this updates the scan path for transcripts and imports immediately.",
-    "placeholder": "/path/to/claude-home",
-    "routersMissing": "Saved. These workspaces name an AI Router profile the new home does not have, and start on Native until it is added there or they are re-pointed: {{lanes}}"
+    "placeholder": "/path/to/claude-home"
   },
   "hooks": {
     "title": "Hook Configuration",
@@ -510,7 +509,6 @@
     "cancel": "Cancel",
     "removeConfirm": "Remove the profile \"{{label}}\"? Every workspace using it is reset to the vendor's own API right away — on disk and in the dashboard.",
     "loading": "Loading profiles…",
-    "lanesFailed": "Saved, but {{count}} workspace could not be updated and still carries the old endpoint: {{lanes}}",
     "test": "Test",
     "testing": "Testing…",
     "testOk": "The endpoint answered — {{model}} is reachable with this key.",
@@ -589,8 +587,7 @@
     "title": "CODEX_HOME",
     "description": "Root directory for Codex config and session journals. The dashboard reads it, writes AI Router layers into it, and starts every codex workspace with it.",
     "restartNote": "A codex workspace already running keeps the home it started with, and shows as idle, until it is restarted.",
-    "placeholder": "/path/to/codex-home",
-    "routersFailed": "Saved, but the AI Router layer could not be re-written for: {{lanes}}"
+    "placeholder": "/path/to/codex-home"
   },
   "codexHooks": {
     "title": "Codex hooks",