iOS VPN will NOT connect on certain WiFi
Most schools have firewalls on their network that prevent VPNs from being used. This is because firewall website filtering can be usually bypassed by using a VPN.

So as you guessed, it is something on the network that’s blocking the VPN.

And just so you know I have not found a way to bypass a VPN blocker or firewall(I am also a student at a school with a similar firewall)