Remove “3rd-party” examples

[wooorm-arcjet]

One goal of the examples here is to make sure that the integrations work in practice.
That a new integration (such as react-router) doesn’t just work in unit tests but also works in practice.
That a new feature (such as filters) works in different places.
These examples catch a change accidentally breaking and also the inverse, help make sure the code here integrates with the latest frameworks.

These examples build in CI and pull the arcjet packages in locally, not from npm, so that things can be developed and verified together.
That’s where the benefit is, over a repo like arcjet/examples.

But pulling in much from the ecosystem also comes with problems:
flakey builds, locked dependencies, messy peer dependencies, slow builds, security “vulnerabilities” unrelated to the code here.

One step to improve the examples in arcjet/arcjet-js is to remove “3rd party” examples.
I propose:

• bun-hono-rate-limit
• express-launchdarkly
• gatsby-rate-limit
• nestjs-fastify
• nestjs-graphql
• nestjs-launchdarkly
• nextjs-14-nextauth-4
• nextjs-authjs-5
• nextjs-authjs-nosecone
• nextjs-better-auth
• nextjs-clerk-rate-limit
• nextjs-clerk-shield
• nextjs-openai
• nextjs-permit
• nextjs-react-hook-form
• nodejs-hono-rate-limit

Q: Are there particular “3rd parties” (hono? gatsby?) that should be kept (somewhere)?

This also closes GH-5110 as it sidesteps that issue.

[blaine-arcjet]

Not all of these should be removed. They can instead be consolidated into a single example, such as the NestJS example can have different entry points to show off Fastify/Express/GraphQL setup.

For the actual 3rd-party integrations, such as OpenAI, Clerk, Permit, Launchdarkly, etc, those all need to be created as public examples before we can remove them. The purpose of the discussion we had during the backlog grooming was not that these would disappear, but that they belong in https://github.com/arcjet/examples where the 3rd-party integrations can be fleshed out and API keys don't cause problems with our CI.