feat(ui): implement pills-style AppSwitcher with consistent button widths

Replace segmented control with pills-style switcher for better visual consistency.

src/components/AppSwitcher.tsx

@@ -0,0 +1,36 @@
+import { AppType } from "../lib/tauri-api";
+import "./AppSwitcher.css";
+
+interface AppSwitcherProps {
+  activeApp: AppType;
+  onSwitch: (app: AppType) => void;
+}
+
+export function AppSwitcher({ activeApp, onSwitch }: AppSwitcherProps) {
+  const handleSwitch = (app: AppType) => {
+    if (app === activeApp) return;
+    onSwitch(app);
+  };
+
+  return (
+    <div className="switcher-pills">
+      <button
+        type="button"
+        className={`switcher-pill ${activeApp === "claude" ? "active" : ""}`}
+        onClick={() => handleSwitch("claude")}
+      >
+        <span className="pill-dot" />
+        <span>Claude Code</span>
+      </button>
+      <div className="pills-divider" />
+      <button
+        type="button"
+        className={`switcher-pill ${activeApp === "codex" ? "active" : ""}`}
+        onClick={() => handleSwitch("codex")}
+      >
+        <span className="pill-dot" />
+        <span>Codex</span>
+      </button>
+    </div>
+  );
+}