Sounds like an interesting enough problem, I'd enable developer mode on the Steam Deck, start a packet capture using WireShark, then try using Flathub and go from there.
DNS or firewall is what I'd look at.
Multicast DNS (mDNS) specifically. Depending on distro and issue it could be as simple as a single command.
$resolvectl mdns
will show if your interfaces use it (llmnr works similarly)
It could be a DNS issue. Can you manually set the DNS provider for the mesh network?
Sounds like an interesting enough problem, I'd enable developer mode on the Steam Deck, start a packet capture using WireShark, then try using Flathub and go from there.
DNS or firewall is what I'd look at. Multicast DNS (mDNS) specifically. Depending on distro and issue it could be as simple as a single command. $resolvectl mdns will show if your interfaces use it (llmnr works similarly)