I've had great success with this.
A bit of understanding networking goes a long way here. (Not sure where you're at as far as that goes.) I'll also start from step 1 just to cover everything.
Update camera and streaming bridge firmware.
The ATEM desktop software has a utility for creating config files. You create a config file that goes onto the camera. This tells the camera where to find the bridge (IP or hostname). I recommend setting a static IP on the streaming bridge and typing that into the config utility (by default it uses hostname).
After you plug in your network adapter ensure you get an IP on the camera itself. You should be able to see the DHCP address in the menu (or if you go static you should be able to ping the camera).
Next, copy your config file to the camera using an SD card and select that profile. Once you start your stream it shouldn't take more than a few seconds to connect.
A few things to note:
Manually modifying the config file is possible (such as to change the IP- no need to be at a computer with the utility to make a new file). It seems the camera ignores the bitrate settings and is fully automatic.
TalkBack audio is one direction only (ATEM to camera).
This is possible to do over WiFi if you use a WiFi to wired bridge like the IOGEAR Universal Ethernet to Wi-Fi Adapter
https://a.co/d/65GkWge (this will take additional config on the device itself before you can plug it into the camera).