Add README for the Vue chat example

[vishxrad]

Summary

examples/vue-chat is the only top-level example without a README. It already has package scripts, an env template, Nuxt/Vue app code, and prompt generation tooling, so this is a good self-contained documentation task.

Suggested content

Add examples/vue-chat/README.md covering:

• what the example demonstrates
• prerequisites
• installing dependencies from the monorepo root
• copying .env.example and setting OPENAI_API_KEY
• generating the prompt if needed
• running pnpm --filter vue-chat dev
• a short project structure section

Useful references:

• examples/svelte-chat/README.md
• examples/vue-chat/package.json
• examples/vue-chat/scripts/generate-prompt.mjs

Acceptance criteria

• examples/vue-chat/README.md exists.
• A new user can follow it to run the example locally.
• The README style is consistent with nearby example READMEs.