Why does the iMac has two IP addresses registered

This is usually down to the router involved, and a security setting disallowing traffic from machines connected to the Wifi interface to the (technically) more secure LAN interface.

If you provide more information on your router manufacture, model we may be able to assist more.

You can adjust the order of your network interfaces in the Network panel of System Preferences. This allows you to set the primary adaptor for your network location, which in your case should be the Wi-Fi adaptor, since that provides the actual correct default route to the Internet.

The re-ordering UI is accessible by clicking on the 'gear' icon below the list of Network Adaptors on the left side of the Network Panel, and choosing "Set Service Order...".

You'll probably want to make & use a new Network Location for this setup, because in general (where either Ethernet or Wi-Fi provide valid default routes to the Internet), the Ethernet will be the better preference.

The same re-ordering can be useful for slightly unusual network setups, or VPNs where you may actually want all traffic to go through the VPN route (ie it should be the first service in the list) or maybe you only want the local subnet traffic on the VPN (ie your standard ethernet/wi-fi connections should precede it).