Setting up MQTT in Home Assistant Container

Use the integration

HA >> settings >> devices and services >> add integration >> mqtt

When connecting docker containers I use the host name of container as this prevents issues if docker decides to change the docker IP. By using this method you only need expose ports if connecting outside docker network

You can use portainer to set hostame if you did not do so during container creation

EDIT

If it is not clear, the integration will connect to the mosquitto container you setup.