I too needed a long time before I knew how to get a printer and scanner working while online when using a VPN with either OpenVPN or Eddie the Client of AirVPN.
Well the answer is much simpler than you think. You need to give your printer an IP4 address that does not change. Like 192.168.1.123 as long as you always make sure it looks like your Router IP4 Gateway adress.
My printer has IP address 192.168.1.123 and if you don't understand how to do that either from within your router DHCP or from the printer itself I cannot help you unfortunately. My printer is simply at this IP4 address via a Wireless Wifi connection at the same router which has address 192.168.1.1 as most Routers do. But yours might look different.
The problem with Windows 10 automatic discovery of printers and scanners it searches all network adapters and it might detect your printers and scanners even like it does here, but when on VPN I couldn't print or scan. Actually the scanner didn't even work before I knew the tricks how to install the same printer manually from an IP4 address by hand.
In Windows 10 right click the start button if your right handed with your right mouse button and enter command below:
I would have liked to show a screenshot here but my language isn't English, so I describe that after you execute that command a Window pops up showing you devices like printers and scanners even when they might not work.
Now look carefully inside that window, what does it say?
but then in your language. Well press that button.
Another window pops up trying to discover devices on your network, but you should look for and press the text
PRINTER I WANT IS NOT ON THIS LIST
Now the magic starts to happen. It has many options to add a Printer, but you know you want a local network printer search for
ADD PRINTER WITH TCP/IP ADDRESS
But then again it is in your own language but look for TCP/IP and press that option. Then press NEXT button.
Another window pops up, leave automatic detection enabled. And guess what, it asks for the IP4 address for your printer, don't worry about port name that will be automatically filled.
Type in your Printer IP4 address inside the IP text Area
was my Printer IP4 address on my local network.
Then it might ask for a driver, if you have none choose a printer that is a version higher but of same type. If you have a Deskjet choose a similar Deskjet, if you have a Laser choose a similar Laser. In my case I simply had the original driver which actually isn't necessary at all.
If your printer is 4000 series and you see a driver called 4070 series try that, as long as it is the same brand of printer and same type of printer (Deskjet=Deskjet and Laser=Laser etcetera) Usually you don't need a driver at this point. Wireless printers communicate with a standard protocol hence Linux Operating Systems almost always too easily support printers and scanners.
Then you have to press a few times NEXT, NEXT and maybe another NEXT.
Make sure you remember how your new manually added printer that only communicates inside your local network outside any VPN is called.
Software using printers or scanners like a webbrowser need a simple adjustment. That is when you print you must select the new printer or scanner you just added by hand.
Please let me know if this works for you, and if you are English, can you do these steps with screenshots and place them in yours? I have a strange language you don't understand, So hence my screenshots would not explain it to you, but in English it does. I cannot for example tell you how to access the configuration panel in your language but that is why I told you it all starts with a simple command to execute
In my case my scanner wasn't even working without VPN and when I executed MSPAINT.EXE, I could even scan wireless when either with or without VPN enabled or disabled. Before I could only print or install hundreds of Megabytes from HP Printer Driver.
Remember the name and IP4 address from your printer that is all you need. Don't rely on auto detection when on VPN.