Simplify and streamline examples

[wooorm-arcjet]

Some dependencies such as tailwind, radix-ui, lucide-react make it harder to maintain but don’t add much (similar arguments as #5220).

Instead, I think it would be good to streamline the examples so that they look like each other (with some minimal regular CSS) and show similar features.
So that humans can compare exactly what’s different for Arcjet between integrations.
This relates a lot to arcjet/examples#5 and also to the comments on the parent issue GH-72.

[davidmytton]

I think most of those come in from a default framework install e.g. Next.js installs various things and includes graphics as well. Agreed on slimming them down to avoid dependencies that aren't relevant to our SDK codebase.

[morekid]

I think it's best to properly brainstorm examples in general and mock a design, layout and feature showcase approach that is consistent. See https://www.notion.so/arcjet/2025-08-28-Design-agenda-25c9ddf35eaf8024b8fadf1b26243c97?source=copy_link#25c9ddf35eaf8057aae0c6682f201acf.

We can then think about how to make the implementation more lightweight and maintainable once we have properly decided how these should look. In scope for this also a consideration to make the DS public so that we can use that.