I'm not at all familiar with these little "repeaters" that you have, but they seem to be similar to each other. Information found with Google is pretty vague, or some unclear Chinese instructions. Have you ever had either of these working? Or are they currently working?
If you've never had them working before, or not working now... some info I found hints that you may have a WPS button on one of them, the WS-WN523N2 model. You could try the WPS connection as
@dos2unix described, and that might bring it to life.
Or you can try to enable one of them manually. The Vonets model shows in your screenshot a web address. If you plug the device into a power outlet, and plug your Linux computer into the LAN port with an ethernet cable.... open up Firefox and type in the URL,
http://vonets.cfg and hit Enter. It should open up a configuration screen on the repeater. If that fails, you can try the URL,
http://192.168.254.254, and hit Enter. Either of these should work, with any luck. If prompted, username is admin, and password is admin, unless you have changed them previously. You should change them now... someone nearby might easily break into your home network through this device with those standard passwords.
Inside the configuration it may get confusing with so little clear info available. You want to scan for your WiFi network.... if you see it, click on it and provide the password to your home router. If you can get this connection established, either manually or with WPS, you may be able to access the internet with the LAN port connected to your Linux computer. You may need to reboot the Linux computer after setting up the repeater. Linux will (almost) always connect to ethernet connections without any effort.... it just works. If you carry the Linux computer to be close to the router and connect it directly with an ethernet cable, you would see this, but I'm unsure about the repeater devices.
The repeater devices may have 3 "modes" available, and I'm again unsure which would be best.
@dos2unix might advise better about that. The modes are "repeater, access point, and router." To me, router mode seems like the last thing to try, as a router would need a different subnet, I think. Sorry, I'm babbling now.
You may have your new WiFi dongle by the time you get one of these working!