Add invite code registration system for beta

Backend:
- Add InviteCode model with single-use codes
- Add invite API endpoints (create, list, revoke, validate)
- Modify registration to require invite code when enabled
- Add REQUIRE_INVITE_CODE config toggle (default: true)
- Add Alembic migration for invite_codes table

Frontend:
- Add invite code field to registration page
- Validate invite code on blur with visual feedback
- Pass invite code to registration API

Admins can generate invite codes via /api/docs (Swagger UI).

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

frontend/src/api/index.ts

@@ -2,3 +2,4 @@ export { default as apiClient } from './client'
 export { default as authApi } from './auth'
 export { default as treesApi } from './trees'
 export { default as sessionsApi } from './sessions'
+export { default as inviteApi } from './invite'

frontend/src/api/invite.ts

@@ -0,0 +1,11 @@
+import apiClient from './client'
+import type { InviteCodeValidation } from '@/types'
+
+export const inviteApi = {
+  async validateCode(code: string): Promise<InviteCodeValidation> {
+    const response = await apiClient.get<InviteCodeValidation>(`/invites/validate/${code}`)
+    return response.data
+  },
+}
+
+export default inviteApi