⚡ Live Sandbox: AI Dev Tool: FastAPI Pydantic v2 MicroSaaS

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```python
# AI Dev Tool: FastAPI Pydantic v2 Micro-SaaS Boilerplate
# ================================================
# This is a production-ready boilerplate for building micro-SaaS applications
# using FastAPI, Pydantic v2, and PostgreSQL Vector Search Extension.

from fastapi import FastAPI, Depends
from fastapi.responses import JSONResponse
from pydantic import BaseModel, Field
from typing import List, Optional
from sqlalchemy import create_engine, Column, Integer, String
from sqlalchemy.ext.declarative import declarative_base
from sqlalchemy.orm import sessionmaker, Session
from sqlalchemy.exc import SQLAlchemyError
from psycopg2.extras import Json

# Initialize the FastAPI application
app = FastAPI()

# Define the database connection URL
DATABASE_URL = "postgresql://user:password@host:port/dbname"

# Create a database engine
engine = create_engine(DATABASE_URL)

# Create a configured "Session" class
SessionLocal = sessionmaker(autocommit=False, autoflush=False, bind=engine)

# Create a base class for declarative class definitions
Base = declarative_base()

# Define the User model
class User(Base):
    __tablename__ = "users"
    id = Column(Integer, primary_key

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