docs: add React Router middleware example

[sornapudisuresh]

Summary

• Adds a React Router middleware example to the README for creating a cookie-based Supabase client.
• Closes Add example for using with React Router middleware #149

Test plan

• npm test (102/102 passed)
• Docs read-through against current React Router middleware APIs

[mandarini]

@claude can you do a first pass review of this PR?

[mandarini]

Hi @sornapudisuresh, thank you so much for contributing to Supabase! 💚

This is a great addition! One thing to fix before merging: I tried compiling the supabaseMiddleware snippet against react-router@8.3.0, and the hand-written context type doesn't match React Router's actual type:

context: { set: (key: unknown, value: unknown) => void };

RouterContextProvider.set is actually a generic method keyed on typed Context objects, so assigning supabaseMiddleware to Route.MiddlewareFunction[] (as the home.tsx snippet does) fails to type-check. Could you drop the inline context type and let it be inferred from Route.MiddlewareFunction/Route.args instead? That should resolve it and keep the example copy-pasteable.

Thanks again for taking the time to put this together, contributions like yours are what keep these docs useful for everyone.

[sornapudisuresh]

Thanks @mandarini! Fixed in the latest commit. The middleware now uses React Router’s MiddlewareFunction so request, context, and next are inferred from the framework’s actual types. Prettier passes and all 102 tests pass.