chore: migrate vue-example to Tailwind CSS v4 with Vite plugin

[chaitanyapotti]

Summary

• Migrate the Vue example to Tailwind CSS v4 using @tailwindcss/vite and CSS-based configuration.
• Remove standalone postcss.config.js and tailwind.config.js from the example.
• Update root package-lock.json / package.json as part of the dependency refresh.

Testing

• npm install at repo root
• cd examples/vue-example && npm run build

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Note

Low Risk
Low risk: changes are confined to the examples/vue-example build pipeline and dependency lockfiles, with no impact on runtime auth logic. Main risk is build/regression in the example due to the new Tailwind v4 CSS-based configuration and Vite plugin integration.

Overview
Migrates examples/vue-example to Tailwind CSS v4 by switching to the @tailwindcss/vite plugin and moving Tailwind configuration into src/tailwind.css using @source directives (including a small inline safelist) and a custom dark variant.

Removes the need for standalone Tailwind/PostCSS config files in the example and refreshes dependencies/lockfiles (including root package.json/package-lock.json) to align with the new toolchain.

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