MQTT discovery/component types questions

I’ve been working on a huesyncbox-mqtt bridge. I’ve got it working when I control it strictly with mqtt messages and have made some progress with HA MQTT discovery but I got stuck.

I’m hoping to approximately replicate the UI in the Hue Sync App, which basically has an on/off switch at the top, a start/stop button at the bottom, a brightness slider, and 2 sets of 4 radio buttons (mutuaully exclusive–scenes/game/audio/video, subtle/moderate/high/intense).

I’m not 100% clear on what MQTT device types would be applicable here. I figured a switch for the master on/off, a light for the start/stop + slider (using existing dimmer functionality for the slider), but I’m not really sure how to/if it’s possible to model the radio button sets. Aesthetically, I’d like something similar to Lovelace Fan Control Entity Row but “fan” didn’t feel like the right way.

I started down the path of MQTT device triggers but I can’t figure out how to render them as buttons in Lovelace. Alternatively, is there a concept of a stateful push button (switch/binary sensor)? If so, I can manage them being mutually exclusive via binary sensor changes.

Also to clarify, assuming I create as many ‘devices’ as is necessary to control this box, I can create one lovelace UI component to tie it all together? I’m hoping to have the MQTT-HA discovery be the only HA-specific code in the huesyncbox-mqtt app and rest live in HA components/config.