Comment by jeroenhd

KDE Connect leverages mDNS on the network (non-Bluetooth) side, which relies on broadcasts. That means it'll break across networks without a VPN of some kind. For some VPNs (Wireguard, OpenVPN in TUN mode) that also means connectivity is impossible.

You can, if you want, open ports and configure KDE connect to reach out across the internet (practically only feasible with one device behind your router on IPv4, any on IPv6), but because it doesn't use "real" DNS, you can't just enter a DDNS hostname, you have to specify the full IP address.