feat(web): polish master chat with model selector, params config, and empty state (#519)

Co-authored-by: Jason Woltje <jason@diversecanvas.com>
Co-committed-by: Jason Woltje <jason@diversecanvas.com>

apps/web/src/components/chat/ChatOverlay.test.tsx

@@ -250,6 +250,46 @@ describe("ChatOverlay", () => {
     });
   });
 
+  describe("new conversation button", () => {
+    it("should render the new conversation button when chat is open", async () => {
+      const { useChatOverlay } = await import("../../hooks/useChatOverlay");
+      vi.mocked(useChatOverlay).mockReturnValue({
+        isOpen: true,
+        isMinimized: false,
+        open: mockOpen,
+        close: mockClose,
+        minimize: mockMinimize,
+        expand: mockExpand,
+        toggle: mockToggle,
+        toggleMinimize: mockToggleMinimize,
+      });
+
+      render(<ChatOverlay />);
+
+      const newConvBtn = screen.getByRole("button", { name: /new conversation/i });
+      expect(newConvBtn).toBeDefined();
+    });
+
+    it("should have a tooltip on the new conversation button", async () => {
+      const { useChatOverlay } = await import("../../hooks/useChatOverlay");
+      vi.mocked(useChatOverlay).mockReturnValue({
+        isOpen: true,
+        isMinimized: false,
+        open: mockOpen,
+        close: mockClose,
+        minimize: mockMinimize,
+        expand: mockExpand,
+        toggle: mockToggle,
+        toggleMinimize: mockToggleMinimize,
+      });
+
+      render(<ChatOverlay />);
+
+      const newConvBtn = screen.getByRole("button", { name: /new conversation/i });
+      expect(newConvBtn.getAttribute("title")).toContain("Cmd+N");
+    });
+  });
+
   describe("responsive design", () => {
     it("should render as a sidebar on desktop", () => {
       render(<ChatOverlay />);