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.

server/lib/pty-run.js

@@ -30,7 +30,7 @@
  */
 
 const tmux = require("./tmux");
-const { routerArgvForSpawn, routerEnvForSpawn } = require("./router-apply");
+const { resolveRouter, routerForSpawn } = require("./router-apply");
 const { desktopEnv } = require("./desktop-env");
 const { getCodexHome } = require("./codex-home");
 const aiTools = require("./ai-tools");
@@ -111,6 +111,7 @@ function buildClaudeArgv({
   initialPrompt,
   addDirs = [],
   systemPromptFile = null,
+  routerArgv = [],
 }) {
   const argv = ["claude"];
   // `--add-dir` is VARIADIC (`<directories...>`): it swallows every following
@@ -118,6 +119,8 @@ function buildClaudeArgv({
   // always ends it — after the prompt it would eat the prompt as a directory.
   if (addDirs.length) argv.push("--add-dir", ...addDirs);
   argv.push("--permission-mode", permissionMode || "auto");
+  // The session's AI Router: `--settings=<file>` (router-apply.js).
+  argv.push(...routerArgv);
   // Claude Code makes the worktree itself (`.claude/worktrees/<name>`, branch
   // `worktree-<name>`, `.worktreeinclude`, the user's WorktreeCreate hook).
   // `=` form: `-w [name]` takes an OPTIONAL value and would otherwise swallow
@@ -158,7 +161,7 @@ function buildCodexArgv({
   resumeLast,
   bypass,
   initialPrompt,
-  routerProfile,
+  routerArgv = [],
   addDirs = [],
   systemPrompt = null,
   systemPromptFile = null,
@@ -167,7 +170,7 @@ function buildCodexArgv({
   // Before the subcommand and before the prompt: `-p` layers
   // `$CODEX_HOME/<name>.config.toml` over the base config, and an option that
   // lands after the positional prompt is not an option any more.
-  argv.push(...routerArgvForSpawn({ tool: "codex", router_profile: routerProfile }));
+  argv.push(...routerArgv);
   if (resumeSessionId) argv.push("resume", resumeSessionId);
   else if (resumeLast) argv.push("resume", "--last");
   if (model) argv.push("-m", model);
@@ -242,8 +245,9 @@ function buildArgv(args, entry) {
  * @param {boolean} [args.bypass] the user ticked "bypass permissions" for THIS
  *   run; appends the catalog's bypass args/env. Claude has no catalog bypass.
  * @param {string} [args.initialPrompt]
- * @param {string} [args.routerProfile] AI Router profile the LANE runs against
- *   (`lanes.router_profile`), never a request field.
+ * @param {string} [args.router] AI Router profile THIS session runs on — a
+ *   name only, its key and endpoint come from the store; null/"native" = the
+ *   vendor's own API. Claude and Codex only (`EUNSUPPORTED`).
  */
 function spawnRun(args) {
   const {
@@ -263,7 +267,7 @@ function spawnRun(args) {
     resumeLast,
     bypass,
     initialPrompt,
-    routerProfile,
+    router,
   } = args || {};
   if (typeof laneId !== "number" || !Number.isInteger(laneId)) {
     throw makeErr("EBADLANE", "laneId must be an integer");
@@ -315,6 +319,7 @@ function spawnRun(args) {
   if (worktree === true && entry.launcher !== "claude") {
     throw makeErr("EUNSUPPORTED", `${tool} cannot start a session in its own worktree`);
   }
+  const routerProfile = resolveRouter(tool, router); // ENOTFOUND, EUNSUPPORTED
   if (forkSession === true) {
     if (!resumeSessionId) throw makeErr("EBADSESSION", "a fork needs resumeSessionId");
     if (entry.launcher !== "claude") {
@@ -351,6 +356,7 @@ function spawnRun(args) {
     laneId,
     tool
   );
+  const routerSpawn = routerForSpawn(tool, routerProfile);
   const argv = buildArgv(
     {
       addDirs,
@@ -368,7 +374,7 @@ function spawnRun(args) {
       resumeLast,
       bypass: bypass === true,
       initialPrompt,
-      routerProfile,
+      routerArgv: routerSpawn.argv,
     },
     entry
   );
@@ -394,6 +400,7 @@ function spawnRun(args) {
       effort: effort || null,
       resumeSessionId: resumeSessionId || null,
       worktree: worktree === true || inWorktree === true,
+      router: routerProfile ? routerProfile.name : null,
       prompt: initialPrompt || "",
       status: "running",
       startedAt,
@@ -407,9 +414,9 @@ function spawnRun(args) {
   // from inside it then resolves the lane exactly, instead of matching on cwd —
   // which is ambiguous now that one directory can back both a `claude` lane and
   // a `codex` lane (see bin/agenthub.js's resolveLaneArg).
-  // A codex lane on an AI Router also needs the key its layer's `env_key`
-  // names. A claude lane needs nothing here — its settings file already carries
-  // the router — and a lane on the vendor's own API needs nothing either.
+  // A codex session on an AI Router also needs the key its layer's `env_key`
+  // names. A claude one needs nothing here — its `--settings` file carries the
+  // router — and a session on the vendor's own API needs nothing either.
   // The graphical session's own DISPLAY/WAYLAND_DISPLAY goes in too: the
   // server normally runs as a systemd user service with neither, so a pane it
   // starts has no clipboard at all — pasting an image into `claude` there
@@ -430,7 +437,7 @@ function spawnRun(args) {
     // journals and the router layer `-p <name>` loads live there — and the
     // tmux server's own env may predate, or never have had, CODEX_HOME.
     ...(tool === "codex" ? { CODEX_HOME: getCodexHome() } : {}),
-    ...routerEnvForSpawn({ tool, router_profile: routerProfile || null }),
+    ...routerSpawn.env,
     ...(bypass === true && entry.bypassEnv ? entry.bypassEnv : {}),
   };