Docs unclear on connection pool vs. direct connection

In the docs under "Supabase" it teaches you how to setup Drizzle w/ supabase. The last part shows how to set up the connection:

import { drizzle } from 'drizzle-orm/postgres-js'
import postgres from 'postgres'
import { users } from './schema'
 
const connectionString = process.env.DATABASE_URL
const client = postgres(connectionString)
const db = drizzle(client);
 
const allUsers = await db.select().from(users);

import { drizzle } from 'drizzle-orm/postgres-js'
import postgres from 'postgres'
import { users } from './schema'
 
const connectionString = process.env.DATABASE_URL
const client = postgres(connectionString)
const db = drizzle(client);
 
const allUsers = await db.select().from(users);

import { drizzle } from 'drizzle-orm/postgres-js'
import postgres from 'postgres'
import { users } from './schema'
 
const connectionString = process.env.DATABASE_URL
const client = postgres(connectionString)
const db = drizzle(client);
 
const allUsers = await db.select().from(users);

import { drizzle } from 'drizzle-orm/postgres-js'
import postgres from 'postgres'
import { users } from './schema'
 
const connectionString = process.env.DATABASE_URL
const client = postgres(connectionString)
const db = drizzle(client);
 
const allUsers = await db.select().from(users);

But underneath it simply says:

Connect to your database using the Connection Pooler for serverless environments, and the Direct Connection for long-running servers.

I'm assuming the code above is for Direct Connection? If that is the case, why is there no implementation demonstration for the Connection Pooler? Also isn't Supabase always going to be serverless? Maybe I'm missing something but this just feels confusing

Docs unclear on connection pool vs. direct connection

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