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/types/index.ts

@@ -2,6 +2,7 @@ export * from './user'
 export * from './auth'
 export * from './tree'
 export * from './session'
+export * from './invite'
 
 // API response wrapper types
 export interface PaginatedResponse<T> {

frontend/src/types/invite.ts

@@ -0,0 +1,4 @@
+export interface InviteCodeValidation {
+  valid: boolean
+  message: string
+}

frontend/src/types/user.ts

@@ -15,6 +15,7 @@ export interface UserCreate {
   password: string
   name: string
   role?: UserRole
+  invite_code?: string
 }
 
 export interface UserLogin {