Setting up Zigbee network on 4 floors: ZHA or HA supported Zigbee GW?

Perfectly right.

However, if you don’t need to move your ZB devices from one ZB network to another(eg. Motion sensors from garage will never need to connect to the roof ZB bridge), then you can link multiple ZB Bridges(each with it’s own network) to HA using multiple instances of Zigbee2MQTT. This is perfectly doable, and I have described almost everything, including config files here: Zigbee ZHA, are multiple coordinators possible? - #11 by mccasian