feat(workspace): AI tool per session, one place to start a session, ended sessions open like Claude Desktop

- A session picks its own AI tool: `tool` on POST /api/lanes/:id/start
  (a catalog id, known + enabled, else 400 EBADTOOL/EDISABLED); a resume
  keeps the tool its session ran on (`sessions.tool`). The workspace's
  `lanes.tool` is now only the default.
- The workspace home's prompt box is the one place a session starts. Its
  fields run in order: AI → AI Router (Native or a profile) → Model (the
  tool's own list, or the router's models) → Permission (Claude mode /
  Codex sandbox+approval / catalog bypass) → Effort.
- The pane's run form (RunSetup) is gone: New run, a single pane's exit and
  an empty split pane's New session all go to the home. RunSetup.tsx keeps
  PromptEditor, CwdAutocomplete and ModelPicker (new `choices` prop).
- The tool icon moved from the sidebar's workspace row to each session row
  (right edge, `session.tool`); the split-pane header shows the run's tool.
- An ended session opens in its workspace (`&session=`, SessionReplay.tsx):
  its conversation read-only plus a prompt box; only a SENT message resumes
  it (resumeSessionId + prompt, first free slot). The console is only
  hidden behind it.
- Analyst button beside Files/Changes in the right panel opens
  /sessions/:id for the opened session.
- Gemini CLI ships its own icon (client/public/ai-tools/gemini.svg, from
  zonalogo.com).
- RouterPicker always shows (Native disabled for tools without router
  support); useAiRouters() exported.
- Tests: server start-with-tool cases; SessionReplay, home field order/tool/
  router models, empty pane, Analyst; dropped the cwd-field suites
  (Run.defaultCwd, Workspace.laneCwd). Docs: CLAUDE.md rules, API.md,
  LANES.md, README, ARCHITECTURE, INSTALL.

client/src/components/run/RouterPicker.tsx

@@ -1,14 +1,15 @@
 /**
  * @file RouterPicker.tsx
  * @description The AI Router a NEW session starts on — a session's choice, not
- * its workspace's (`router` on `POST /api/lanes/:id/start`, `server/lib/router-apply.js`).
- * Shown only for a tool that can use one (Claude, Codex) and only when a
- * profile beyond Native exists. The last pick is remembered for the next
- * session (`agenthub.session.router`).
+ * its workspace's (`router` on `POST /api/lanes/:id/start`, `server/lib/router-apply.js`):
+ * Native or one of the saved profiles (`useAiRouters`, which the caller also
+ * reads to list the router's models). A tool that cannot use a router (only
+ * Claude and Codex can) shows Native, disabled. The last pick is remembered
+ * for the next session (`agenthub.session.router`).
  * @author Nguyễn Ngọc Trí Vĩ <vinnt@smartgift.vn>
  */
 
-import { useEffect, useState, type ReactNode } from "react";
+import { useEffect, useState } from "react";
 import { useTranslation } from "react-i18next";
 import { api, type AiRouter } from "../../lib/api";
 import { useAiTools } from "../../hooks/useAiTools";
@@ -36,28 +37,9 @@ export function useSessionRouter(): [string, (v: string) => void] {
   return [value, set];
 }
 
-/** What to send as `router` for `tool`: nothing for native or a tool that has none. */
-export function routerArg(routerCapable: boolean | undefined, router: string): { router?: string } {
-  return routerCapable && router && router !== "native" ? { router } : {};
-}
-
-export function RouterPicker({
-  tool,
-  value,
-  onChange,
-  wrap = (el) => el,
-}: {
-  tool: string;
-  value: string;
-  onChange: (v: string) => void;
-  /** Puts the select in the caller's labelled field; not called while hidden. */
-  wrap?: (select: ReactNode) => ReactNode;
-}) {
-  const { t } = useTranslation(["lanes"]);
-  const aiTools = useAiTools();
-  const capable = aiTools.byId(tool)?.routerCapable ?? (tool === "claude" || tool === "codex");
+/** The saved profiles (Native included), null until they arrive. */
+export function useAiRouters(): AiRouter[] | null {
   const [routers, setRouters] = useState<AiRouter[] | null>(null);
-
   useEffect(() => {
     let alive = true;
     api.aiRouters
@@ -68,6 +50,30 @@ export function RouterPicker({
       alive = false;
     };
   }, []);
+  return routers;
+}
+
+/** What to send as `router` for `tool`: nothing for native or a tool that has none. */
+export function routerArg(routerCapable: boolean | undefined, router: string): { router?: string } {
+  return routerCapable && router && router !== "native" ? { router } : {};
+}
+
+export function RouterPicker({
+  tool,
+  routers,
+  value,
+  onChange,
+}: {
+  tool: string;
+  /** From `useAiRouters`. */
+  routers: AiRouter[] | null;
+  value: string;
+  onChange: (v: string) => void;
+}) {
+  const { t } = useTranslation(["lanes"]);
+  const aiTools = useAiTools();
+  const capable = aiTools.byId(tool)?.routerCapable ?? (tool === "claude" || tool === "codex");
+  const native = t("router.native", { tool: aiTools.label(tool) });
 
   // A remembered profile that has since been deleted falls back to native,
   // or the start would be refused for a router the user cannot see.
@@ -75,16 +81,17 @@ export function RouterPicker({
     if (routers && value !== "native" && !routers.some((r) => r.name === value)) onChange("native");
   }, [routers, value, onChange]);
 
-  if (!capable || !routers || routers.length <= 1) return null;
-  return wrap(
-    <div className="w-44" data-testid="router-picker" title={t("router.label")}>
+  const options =
+    capable && routers?.length
+      ? routers.map((r) => ({ value: r.name, label: r.builtin ? native : r.label }))
+      : [{ value: "native", label: native }];
+  return (
+    <div data-testid="router-picker" title={t("router.label")}>
       <Select<string>
-        value={value}
+        value={capable ? value : "native"}
         onChange={onChange}
-        options={routers.map((r) => ({
-          value: r.name,
-          label: r.builtin ? t("router.native", { tool: aiTools.label(tool) }) : r.label,
-        }))}
+        options={options}
+        disabled={!capable}
       />
     </div>
   );