feat: model lists and prices that follow each AI tool, a Settings tab per tool, live lane status (#40)

Pricing: the LiteLLM sync now adds every current Claude / GPT (>= 5) /
Gemini (>= 3) chat model before it is used and keeps its own rows
(model_pricing.source = 'sync', the Auto badge) at the published rate. A
user's row (any PUT) and a deleted pattern (model_pricing_dismissed) are
never touched; a deleted built-in row is not re-seeded at the next start; a
reset re-applies the list at once; retired Claude models are priced only
once used.

Models: GET /api/ai-tools/:id/models reads each tool's own list (Codex's
models_cache.json, Claude's aliases named after the newest version plus
priced versions, a catalog tool's vendor rows plus the models its sessions
used). A catalog `model: {flag, vendor?}` field passes `<flag> <id>`
(validated: never a flag or shell text); a per-tool default model starts
each run, and a resume keeps the session's own model.

Settings: every installed, enabled catalog tool without its own tab gets
one (AiToolConfig.tsx): path, homepage, Update, sessions/cost/lanes,
default model, vendor pricing, and the config files its release catalog
lists, edited over the opened sha, syntax-checked, backed up, written
atomically; credential-looking names refused. Antigravity keeps its hooks
card there.

Lanes: a just-started run no longer reads "dead" (age counts the run's
start while the old session is still bound); a second dashboard on the
same database re-broadcasts the lanes the other changed (PRAGMA
data_version, every 2 s); a lane start with a bad model answers 400.

DB: every migration runs under a cross-process lock (<db>-migrate.lock), so
two dashboards started at once on a fresh database both come up.

client/src/components/settings/__tests__/AiToolsSettings.test.tsx

@@ -54,6 +54,10 @@ const tool = (id: string, label: string, over: Partial<AiTool> = {}): AiTool =>
   routerCapable: false,
   install: null,
   update: null,
+  modelFlag: false,
+  defaultModel: null,
+  modelVendor: null,
+  configFiles: 0,
   ...over,
 });
 const VIEW: AiToolsView = {
@@ -257,6 +261,28 @@ describe("SettingsHub — AI tool tabs", () => {
     expect(screen.queryByRole("tab", { name: /^Codex/ })).toBeNull();
   });
 
+  it("gives every installed, enabled catalog tool its own tab, and none to the rest", async () => {
+    vi.mocked(api.aiTools.list).mockResolvedValue({
+      default: "claude",
+      tools: [
+        tool("claude", "Claude Code", { launcher: "claude" }),
+        tool("gemini", "Gemini"),
+        tool("qwen-code", "Qwen Code", { enabled: false }),
+        tool("aider", "Aider", { installed: false }),
+      ],
+    });
+    vi.doMock("../../../pages/Settings", () => ({ Settings: () => null }));
+    const { SettingsHub } = await import("../../../pages/SettingsHub");
+    render(
+      <MemoryRouter>
+        <SettingsHub />
+      </MemoryRouter>
+    );
+    expect(await screen.findByRole("tab", { name: /Gemini/ })).toBeInTheDocument();
+    expect(screen.queryByRole("tab", { name: /Qwen Code/ })).toBeNull();
+    expect(screen.queryByRole("tab", { name: /Aider/ })).toBeNull();
+  });
+
   it("opens AI Tools as a modal from the tab bar, and closes it on Escape", async () => {
     vi.doMock("../../../pages/Settings", () => ({ Settings: () => null }));
     const { SettingsHub } = await import("../../../pages/SettingsHub");