Better question is what is not compatible with HA? Not trying to be funny
But alot will work with HA, for example HUE stuff if you have the HUE bridge, Wifi lights (out of the box and with a hack), your TV/sonos
Your car. I could go on, but what do you want todo first?
Most “smart” devices that connect to your network will work.
From my total-noob-experience everything that speaks MQTT is extremely likely to be integrated in HA. Here it is my lawnmower, a relay board hacking my heating system, next step is a barebone sensor connected through an ESPHome board. My photovoltaic system speaks Modbus but integration was done in 5min. My automatic lawn watering system can be integrated. My Internet modem (FritzBox) always offers full integration, my TV offers it, etc.
Just browsing through a list of integrations always leaves me like “WOW how can THAT be integrated in HA?”
Without a Zigbee stick yes, since HUE for the most part is Zigbee (a few bluetooth only devices)
Tho i would do it with the Zigbee stick since HUE now requires registration.
For a complete list of things that work see: Integrations - Home Assistant
MQTT is just a middle man, HA supports MQTT so any device that supports MQTT can send messages to HA via a MQTT server
You have to decide what communication protocol you wanna use. You can use wifi, zigbee, bluetooth, rf, and as I always forget z-wave. People usually are using wifi or zigbee some of them z-wave while bluetooth and rf is less common.
What will you use depends on you infrastructure and preferences. You have to understand that you are building a network of devices and you will have to think about pros and cons of every option before you make decision.
if you are planing to have just a few devices that it doesn’t actually matter as everything will work just fine.
OK. So if you absolutely do not want to consider another zigbee or z-wave stick, then the wifi devices would probably your best bet. (better than bluetooth, anyways.)
Given that you are in EU, I would recommend you look into Shelly devices. They sure should have products for what you have in mind. Shelly.com
Final note form me: Maybe not now, but sometime down the road, you might want to look into zigbee or z-wave. It would be fun.
After all, the best part of going HA is that you can bring devices from different protocols together under the same umbrella, so that z-wave motion sensors can trigger wifi light switches, plus zigbee thermostatic radiator valves, while considering weather data from the internet, etc.
Like I said, it would be fun.
for temperature you have a lot of options,
Swtichbot temperature meter if you want a larger screen.
Xiamoi Temperature sensor with custom firmware, (can be flashed with Bluetooth only, zigbee only and zigbee + Bluetooth firmware).
Inkbird thermometer a little expensive without the screen and has its uses e.g in freezer
for radiators, you have smart switches Wifi/zigbee/Z-wave. There are so many form factors with power monitoring and without power monitoring. just search Amazon/aliexpress/your local online store/supermarket / electronic market.