When I connect to VPN in Windows 10 and then change the gateway setting of default ethernet connection, will VPN remain to route traffic through the gateway it has on connection moment or will use new one?
It will use the new default gateway.
Assuming that it works at the OS level (as opposed to, for example, anonymization services which describe themselves as VPNs but are really something very different) connecting to a vpn will create a new, virtual interface on your machine. This will acquire new routes. The gateway used by a machine depends on the routes configured - so some traffic may continue to be routed through the original interface/gateway (based on the target IP address) while some (or possibly all) will be routed via a gateway configured against the new interface. Running 'route -n' at the command prompt will show you what is currently in place.
If you manually change the route after establishing the VPN connection then the traffic wil follow the rules defind in the new routing table.