Fix Lit dependency duplication and update mini-lit to 0.2.0

- Move lit from dependencies to peerDependencies in web-ui to prevent multiple Lit instances being loaded
- Update mini-lit from 0.1.8/0.1.10 to 0.2.0 in root package.json and web-ui/package.json
- Install @tailwindcss/vite in web-ui/example
- Run biome formatting fixes across codebase

This resolves HMR custom element re-registration errors caused by duplicate Lit registries.

packages/web-ui/example/src/custom-messages.ts

@@ -1,8 +1,8 @@
-import { Alert } from "@mariozechner/mini-lit";
 import type { Message } from "@mariozechner/pi-ai";
 import { html } from "lit";
 import { registerMessageRenderer } from "@mariozechner/pi-web-ui";
 import type { AppMessage, MessageRenderer } from "@mariozechner/pi-web-ui";
+import { Alert } from "@mariozechner/mini-lit/dist/Alert.js";
 
 // ============================================================================
 // 1. EXTEND AppMessage TYPE VIA DECLARATION MERGING

packages/web-ui/example/src/main.ts

@@ -1,4 +1,3 @@
-import { Button, icon, Input } from "@mariozechner/mini-lit";
 import "@mariozechner/mini-lit/dist/ThemeToggle.js";
 import { getModel } from "@mariozechner/pi-ai";
 import {
@@ -26,6 +25,9 @@ import { html, render } from "lit";
 import { Bell, History, Plus, Settings } from "lucide";
 import "./app.css";
 import { createSystemNotification, customMessageTransformer, registerCustomMessageRenderers } from "./custom-messages.js";
+import { Button } from "@mariozechner/mini-lit/dist/Button.js";
+import { icon } from "@mariozechner/mini-lit";
+import { Input } from "@mariozechner/mini-lit/dist/Input.js";
 
 // Register custom message renderers
 registerCustomMessageRenderers();