The original profile sets ipv4.gateway. That is not right.
ipv4.gateway basically means to add a default route to the main table. If you want to route all traffic via the VPN (with allowed-ips=0.0.0.0/0), you must make sure that there is no routing loop. Setting the gateway does just that. Instead, let NetworkManager handle that automatically (via wireguard.ip4-auto-default-route).
All you need is nmcli connection modify "home" ipv4.gateway '' and reactivate the profile with nmcli connection up home.
– Update: man nm-settings also comments about that. See wireguard.ip4-auto-default-route.