wireguard tunnel roaming

I have an app in fly that proxies to another app running in a datacenter (cough my homelab *cough) that has, shall we say, slightly unreliable internet access. I recently set up a failover ISP via LTE tethering and when I was testing I noticed that fly lost connection to my homelab server.

I thought that wireguard was able to roam, but maybe this is too much for it? It ends up being triple NAT’d (CGNAT, LTE phone hotspot, my router), could that be the problem?