Create a Windows “Network Connection” backed by an SSH tunnel

I am using a machine running Windows 10, connected to a LAN using Ethernet. That connection is configured in Windows and working (well, sort of, but that’s not the point in this question). For reasons, I need to route my network traffic over an SSH tunnel. I can set a dynamic SOCKS proxy fine using PuTTY, and applications which explicitly support proxy use – work with it (e.g. my browser). However, not all applications have this support, and I want all apps’ traffic to be routed over this tunnel. So, what I believe I need is a Windows Network Connection, through which I could have Windows route traffic by default.

I believe this is possible since I’ve seen Windows machines with a separation Network Connection for some VPN, different that the physical NICs. So – how can I make that happen? (To be honest, I’m not sure about the routing afterwards, but that should not be too difficult.)

Note: If any additional information is necessary for an answer, please ask for it in the comments.