Thank you.
At the risk of over-simplifying your computer is getting confused between the wifi network and the ethernet network. You should only "connect to one network". You are trying to use two network adapters simultaneously (the wired port and the wireless port). Not the usual or necessary home network set-up.
All devices should get their IP address from the router (device in the upper right hand corner of your sketch) unless there is a requirement for a static IP address. Will set that aside for the moment.
Right now your computer is seeing "two sources" when both the printer and the wireless adapter are active/enabled.
If the printer must be ethernet then the printer's ethernet cable should go directly to the router and not the desktop. That will also allow other devices to print without having to have the desktop powered on.
Is it possible to run an ethernet cable to the router?
If only the desktop needs to print you could use USB to connect the printer and the desktop.
I.e.,
1) Unplug/remove the ethernet cable to the printer and disable that network adapter.
2) Set the printer up using a USB cable and another USB port on the desktop.
Note: other devices could still print if the desktop shares the printer and remains powered on.
Just post any further questions, comments, or concerns. We can go from there....