Installation is unhealthy and cannot install plugins

There is no button to add a sensor, everything is added through mqtt auto-discovery.

Does the sensor exist in Developer Tools / States ?

Go to configuration > integrations > MQTT, click CONFIGURE, then RE-CONFIGURE MQTT, then NEXT and make sure “Enable discovery” is selected. I think it’s disabled by default.

While you’re at it, make sure both “birth message retain” and “will message retain” are checked. Those are disabled by default which is strange.