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>

backend/alembic/versions/002_add_invite_codes.py

@@ -0,0 +1,52 @@
+"""Add invite codes
+
+Revision ID: 002
+Revises: 7e00fa3c75c9
+Create Date: 2026-02-01
+
+"""
+from typing import Sequence, Union
+
+from alembic import op
+import sqlalchemy as sa
+from sqlalchemy.dialects import postgresql
+
+# revision identifiers, used by Alembic.
+revision: str = '002'
+down_revision: Union[str, None] = '7e00fa3c75c9'
+branch_labels: Union[str, Sequence[str], None] = None
+depends_on: Union[str, Sequence[str], None] = None
+
+
+def upgrade() -> None:
+    # Create invite_codes table
+    op.create_table(
+        'invite_codes',
+        sa.Column('id', postgresql.UUID(as_uuid=True), primary_key=True),
+        sa.Column('code', sa.String(16), nullable=False, unique=True, index=True),
+        sa.Column('created_by_id', postgresql.UUID(as_uuid=True), sa.ForeignKey('users.id'), nullable=False),
+        sa.Column('used_by_id', postgresql.UUID(as_uuid=True), sa.ForeignKey('users.id'), nullable=True),
+        sa.Column('expires_at', sa.DateTime(timezone=True), nullable=True),
+        sa.Column('note', sa.String(255), nullable=True),
+        sa.Column('created_at', sa.DateTime(timezone=True), nullable=False, server_default=sa.text('now()')),
+        sa.Column('used_at', sa.DateTime(timezone=True), nullable=True),
+    )
+
+    # Add invite_code_id FK to users table
+    op.add_column('users', sa.Column('invite_code_id', postgresql.UUID(as_uuid=True), nullable=True))
+    op.create_foreign_key(
+        'fk_users_invite_code_id',
+        'users',
+        'invite_codes',
+        ['invite_code_id'],
+        ['id']
+    )
+
+
+def downgrade() -> None:
+    # Remove FK and column from users
+    op.drop_constraint('fk_users_invite_code_id', 'users', type_='foreignkey')
+    op.drop_column('users', 'invite_code_id')
+
+    # Drop invite_codes table
+    op.drop_table('invite_codes')