It seems you picked a fairly complicated system as your first foray into Modbus. It sounds like you have 3 Modbus devices in your system: the heat pump itself, the display, and the WiFi gateway. One of these devices must be the master and the other two are the slaves.
I recommend first determining which device is the master. I believe you've already removed the WiFi gateway and still see communications, so you just need to find out whether the master device is the display or the heat pump. The easiest way to do this is to monitor communications (using LED's or software on your PC) and powering off or removing one of the devices from the network. If there is still communications traffic, the device powered on and connected to the network is the master.
Now the problem:
Home Assistant is very likely a Modbus Master. You can only have one Modbus master on the bus. If you want to connect Home Assistant to a Modbus device, the typical way of doing this is to connect directly to the Modbus device (which must be a Modbus slave) without any other master on the bus (i.e. Home Assistant can be the only Modbus master on the RS-485 bus).
If the display is the master, then you could simply disconnect the display and connect Home Assistant to the heat pump. However, you would have to be alright with not having the display anymore and the WiFi gateway would not work unless you can configure Home Assistant to duplicate the messages that the display sent to the WiFi gateway.
Alternatively, you can connect a gateway to the system that supports "sniffing" the existing Modbus network. This gateway can listen to the communications between the display, heat pump, and WiFi gateway, extract the register values exchanged, and make them available to a separate RS-485 Modbus network. Now keep in mind, though, since the display is the master, you are limited to only being able to "sniff" the registers that the display is requesting.
ICC's Mirius gateway can be used for sniffing a Modbus RTU network and exposing the data to another Modbus RTU master:
http://www.iccdesigns.com/protocol-gateways/66-mirius.html
I recommend first determining which device is the master. I believe you've already removed the WiFi gateway and still see communications, so you just need to find out whether the master device is the display or the heat pump. The easiest way to do this is to monitor communications (using LED's or software on your PC) and powering off or removing one of the devices from the network. If there is still communications traffic, the device powered on and connected to the network is the master.
Now the problem:
Home Assistant is very likely a Modbus Master. You can only have one Modbus master on the bus. If you want to connect Home Assistant to a Modbus device, the typical way of doing this is to connect directly to the Modbus device (which must be a Modbus slave) without any other master on the bus (i.e. Home Assistant can be the only Modbus master on the RS-485 bus).
If the display is the master, then you could simply disconnect the display and connect Home Assistant to the heat pump. However, you would have to be alright with not having the display anymore and the WiFi gateway would not work unless you can configure Home Assistant to duplicate the messages that the display sent to the WiFi gateway.
Alternatively, you can connect a gateway to the system that supports "sniffing" the existing Modbus network. This gateway can listen to the communications between the display, heat pump, and WiFi gateway, extract the register values exchanged, and make them available to a separate RS-485 Modbus network. Now keep in mind, though, since the display is the master, you are limited to only being able to "sniff" the registers that the display is requesting.
ICC's Mirius gateway can be used for sniffing a Modbus RTU network and exposing the data to another Modbus RTU master:
http://www.iccdesigns.com/protocol-gateways/66-mirius.html