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/src/components/Input.ts

@@ -1,4 +1,5 @@
-import { type BaseComponentProps, fc, html } from "@mariozechner/mini-lit";
+import { type BaseComponentProps, fc } from "@mariozechner/mini-lit/dist/mini.js";
+import { html } from "lit";
 import { type Ref, ref } from "lit/directives/ref.js";
 import { i18n } from "../utils/i18n.js";