Can I run CockroachDB as a drop-in replacement for Postgres?

[fwoodruff-ab]

services:
  db:
    container_name: db
    image: postgres:15
    restart: unless-stopped
    ports: 
      - "5432:5432"
    environment:
      - POSTGRES_USER=my_user
      - POSTGRES_PASSWORD=my_password
      - POSTGRES_DB=postgres
    volumes:
      - my-pgdata-db:/var/lib/postgresql/data
      - ./migrations/db_migration.sql:/docker-entrypoint-initdb.d/init.sql
 volumes:
    my-pgdata-db:

I have a vanilla docker-compose.yml file which runs some services against Postgres. Those services use github.com/jackc/pgx/v4 (among other Golang libraries) to talk to those databases, running migrations and then later making modifications and queries.
This link suggests that it might be possible to swap CockroachDB for Postgres without changing the application code.
If I swap postgres:15 for cockroachdb/cockroach:v24.1.2, what other changes should I make so that, as closely as possible, the application code still runs?

Notably, I would like to connect to CockroachDB without TLS but with password login.