I don’t use HassIO/HassOS, but I do use Mosquitto that I installed myself and I do use Zwave2MQTT; So I may not understand completely the setup you have.
My first thought is centered around the authentication.
For the ZWave2MQTT you have the ‘Auth’ enabled, but have you entered a username and password?
I would think for the MQTT Broker you also would need a username and password configured too but doesn’t appear to be there.
Anyway as a first test, turn off all authentication, both Zwave2MQTT and the Broker, just to see if Zwave2MQTT is talking to the broker.
Hmmm…I’m surprised ZWave2MQTT will not let you turn off authentication…
I’m sorry that I don’t know enough about the HassOS implementation of the mosquitto Broker to help. Just reading the wiki, it seems by default the mosquitto broker add-on (I assume you’re using the mosquitto add-on) picks up the username/password of existing HA users, and one of these users (and password) you would select to enter for ZWave2mqtt’s mqtt broker authentication settings. I couldn’t find anything about an auto-generated password, so I may be off base somehow.
As for needing to add units manually for HA, most users have success using the auto-discovery feature of zwave2mqtt, so no should not need to manually configure zwave units into HA if you do auto-discovery.
As for my ZWave2mqtt, My MQTT settings are like yours except I have configured a username and password (which appears under the “Store”/“Auth” buttons), and these settings match that username and password I have setup at mosquitto to allow clients to access it.
As for my mosquitto settings, I don’t use the Add-on, and so the configuration schema can’t be compared. I would suggest you look at the wiki I referred to earlier, and search the Forum for “mosquitto broker add on” (such as this one).