Stroke of luck: I’m just at a public wifi with network address 192.168.0.0/24 with the router at 192.168.0.1. And, connected to my home network (via OpenVPN Server) I can access my router login page at 192.168.10.1. And if, instead, and still connected via OpenVPN, I enter 192.168.0.1 into my browser, I get the (poorly secured) login page for the gateway on this remote public wifi network.
Good point you made about setting the LAN and Internet access at both.
Hmm. Then it is quite weird that I cannot reach 192.168.1.1 on the local network at my cottage when connected to my home VPN.