refactor(auth): switch to class-based social login and v4 route handler

Migrate from function-based social login helpers (`facebookLogin`, `googleLogin`)
to class-based services (`new FacebookLogin().signIn()`, `new GoogleLogin().signIn()`),
updating call sites in `AuthFacebookPanel` and `SplashButton` with try/catch error
handling. The NextAuth route handler is also refactored to the v4 pattern, importing
pre-built `GET` / `POST` exports from `@/lib/auth/nextauth` instead of constructing
the handler inline with `NextAuth(authOptions)`.

docs/nextauth/docs/providers/42.md

@@ -0,0 +1,38 @@
+---
+id: 42-school
+title: 42 School
+---
+
+:::note
+42 returns a field on `Account` called `created_at` which is a number. See the [docs](https://api.intra.42.fr/apidoc/guides/getting_started#make-basic-requests). Make sure to add this field to your database schema, in case if you are using an [Adapter](https://next-auth.js.org/adapters).
+:::
+
+## Documentation
+
+https://api.intra.42.fr/apidoc/guides/web_application_flow
+
+## Configuration
+
+https://profile.intra.42.fr/oauth/applications/new
+
+## Options
+
+The **42 School Provider** comes with a set of default options:
+
+- [42 School Provider options](https://github.com/nextauthjs/next-auth/blob/v4/packages/next-auth/src/providers/42-school.ts)
+
+You can override any of the options to suit your own use case.
+
+## Example
+
+```js
+import FortyTwoProvider from "next-auth/providers/42-school";
+...
+providers: [
+  FortyTwoProvider({
+    clientId: process.env.FORTY_TWO_CLIENT_ID,
+    clientSecret: process.env.FORTY_TWO_CLIENT_SECRET
+  })
+]
+...
+```