Does anyone have experience with equipping an entire house with Smart relay switches (preferably zigbee) as an alternative to wired domotics and managing all this via home assistant? The purpose would be to manage everything in the house (lights, curtains, heating, …) What are advantages and disadvantages?
Not with your preferably zigbee devices but with ESPHome compatible wifi gear instead. 
This is exact what we do… lights, heating, pumps, valves, etc. 
Biggest advantage is probably the outstanding 
price/performance ratio compared to commercially available wired solutions. Beside if your hardware runs ESPHome you are free to change and improve your device as you please and with local push it offers the best possible connection to Home Assistant 
That it is not wired? 
This month ESPHome 2023.09 is scheduled which will bring support for tuya based chips which will probably included this outrageously cheap smart relays 
https://www.aliexpress.com/item/1005005058104691.html