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```python
# AI Dev Tool: FastAPI Pydantic v2 Micro-SaaS Boilerplate with PostgreSQL Vector Search
# ==============================================================================
# This is a production-ready boilerplate for building micro-SaaS applications using FastAPI and Pydantic v2.
# It includes integration with PostgreSQL Vector Search extension for efficient similarity search.

import os
import uvicorn
from fastapi import FastAPI, Depends, HTTPException
from fastapi.security import OAuth2PasswordBearer, OAuth2PasswordRequestForm
from pydantic import BaseModel, EmailStr
from typing import Optional
from sqlalchemy import create_engine, Column, Integer, String
from sqlalchemy.ext.declarative import declarative_base
from sqlalchemy.orm import sessionmaker
from sqlalchemy.exc import SQLAlchemyError
from psycopg2.extras import Json

# PostgreSQL connection settings
POSTGRES_USER = os.environ.get("POSTGRES_USER", "postgres")
POSTGRES_PASSWORD = os.environ.get("POSTGRES_PASSWORD", "postgres")
POSTGRES_HOST = os.environ.get("POSTGRES_HOST", "localhost")
POSTGRES_PORT = os.environ.get("POSTGRES_PORT", 5432)
POSTGRES_DB = os.environ.get("POSTGRES_DB", "postgres")

# Create PostgreSQL engine
engine = create_engine(f"postgresql://{POST

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