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```python
# AI Dev Tool: PostgreSQL Vector Search Extension with FastAPI and Hono
# =====================================================================
# This code asset provides a production-ready PostgreSQL vector search extension
# using FastAPI and Hono. It allows developers to easily integrate vector search
# functionality into their applications.

# Import required libraries
from fastapi import FastAPI, HTTPException
from fastapi.responses import JSONResponse
from fastapi.requests import Request
from fastapi.middleware.cors import CORSMiddleware
from hono import Hono
from psycopg2 import connect
from psycopg2.extras import DictCursor
from typing import Dict, List

# Initialize FastAPI application
app = FastAPI()

# Initialize Hono instance
hono = Hono()

# Define PostgreSQL database connection settings
DB_HOST = "localhost"
DB_NAME = "vector_search_db"
DB_USER = "vector_search_user"
DB_PASSWORD = "vector_search_password"

# Define CORS middleware settings
origins = ["*"]

# Initialize CORS middleware
app.add_middleware(
    CORSMiddleware,
    allow_origins=origins,
    allow_credentials=True,
    allow_methods=["*"],
    allow_headers=["*"],
)

# Define a function to connect to the PostgreSQL database
def connect_to_db
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