feat: add bun-fullstack agent and update skills

.agent/skills/tech-stack/elysiajs/integrations/better-auth.md

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+# Better Auth Integration
+Elysia + Better Auth integration guide
+
+## What It Is
+Framework-agnostic TypeScript auth/authz. Comprehensive features + plugin ecosystem.
+
+## Setup
+```typescript
+import { betterAuth } from 'better-auth'
+import { Pool } from 'pg'
+
+export const auth = betterAuth({
+  database: new Pool()
+})
+```
+
+## Handler Mounting
+```typescript
+import { auth } from './auth'
+
+new Elysia()
+  .mount(auth.handler)  // http://localhost:3000/api/auth
+  .listen(3000)
+```
+
+### Custom Endpoint
+```typescript
+// Mount with prefix
+.mount('/auth', auth.handler)  // http://localhost:3000/auth/api/auth
+
+// Customize basePath
+export const auth = betterAuth({
+  basePath: '/api'  // http://localhost:3000/auth/api
+})
+```
+
+Cannot set `basePath` to empty or `/`.
+
+## OpenAPI Integration
+Extract docs from Better Auth:
+```typescript
+import { openAPI } from 'better-auth/plugins'
+
+let _schema: ReturnType<typeof auth.api.generateOpenAPISchema>
+const getSchema = async () => (_schema ??= auth.api.generateOpenAPISchema())
+
+export const OpenAPI = {
+  getPaths: (prefix = '/auth/api') =>
+    getSchema().then(({ paths }) => {
+      const reference: typeof paths = Object.create(null)
+      
+      for (const path of Object.keys(paths)) {
+        const key = prefix + path
+        reference[key] = paths[path]
+        
+        for (const method of Object.keys(paths[path])) {
+          const operation = (reference[key] as any)[method]
+          operation.tags = ['Better Auth']
+        }
+      }
+      
+      return reference
+    }) as Promise<any>,
+  components: getSchema().then(({ components }) => components) as Promise<any>
+} as const
+```
+
+Apply to Elysia:
+```typescript
+new Elysia().use(openapi({
+  documentation: {
+    components: await OpenAPI.components,
+    paths: await OpenAPI.getPaths()
+  }
+}))
+```
+
+## CORS
+```typescript
+import { cors } from '@elysiajs/cors'
+
+new Elysia()
+  .use(cors({
+    origin: 'http://localhost:3001',
+    methods: ['GET', 'POST', 'PUT', 'DELETE', 'OPTIONS'],
+    credentials: true,
+    allowedHeaders: ['Content-Type', 'Authorization']
+  }))
+  .mount(auth.handler)
+```
+
+## Macro for Auth
+Use macro + resolve for session/user:
+```typescript
+const betterAuth = new Elysia({ name: 'better-auth' })
+  .mount(auth.handler)
+  .macro({
+    auth: {
+      async resolve({ status, request: { headers } }) {
+        const session = await auth.api.getSession({ headers })
+        
+        if (!session) return status(401)
+        
+        return {
+          user: session.user,
+          session: session.session
+        }
+      }
+    }
+  })
+
+new Elysia()
+  .use(betterAuth)
+  .get('/user', ({ user }) => user, { auth: true })
+```
+
+Access `user` and `session` in all routes.