If you uninstall the addon it removes the persistence database and settings.
You didn’t say what kind of devices you are using.
My broker is configured like this:
See no login so it uses a HA user to authenticate:
I created a Home Assistant user MQTT-User and I use that username and password in all my devices to authenticate.
IF you are using something other than that kind of setup that may be your problem. It could also be that you need to setup an accesscontrol list and acl.conf file but you shouldn’t need that.