I understand your goal. I've run this solution for more than a decade, originally with openvpn and multiple subnets.

Yes, it does require your local networks to be subnets of the VPN. If you can't control dhcp, then you can add static alias IPs to the local interfaces and thus have "another" local subnet for this purpose. In these cases, the wireguard link might need two addresses (AllowedIPs: 10.x.x.x/31) where one of them is configured on the local interface with the local subnet mask, the wireguard ip configured with the wider VPN mask.

Adding IP aliases doesn't seem to be possible on phones though ...