Does the school you go to need to know that you have the Signal app installed on your phone, checking with the Signal servers in the background for new messages? Even if you chose to use a VPN to tunnel your traffic entirely, is there no other option but for your employer to witness you connected to a foreign VPN server? If you connected to a point at your home, even that could be interpreted that you have something hide.
You could have two phones with different sets of apps in your pocket (one for “business” and one for everything else), but you if you don’t want that you have to ask:
Is there a firewall for Android that can block your usual traffic from leaving the device, by turning on a specific profile based on something like the Wi-Fi name? There are quite a few traffic blockers, such as RethinkDNS, Netguard, or personalDNSfilter, but they assume you want to block the same set of traffic regardless of time and place.
Surely the simplest approach is not to use a wifi ssid that you don’t trust. Yes, mobile broadband is slower and more expensive, but is also more under your control, it is however harder for your boss to monitor.
If I was an it manager I’d probably want to keep an eye on WiFi traffic, even on the open ssid, just to see what’s going on. I don’t trust free WiFi.
If you can’t use 4/5g, and can’t find a suitable firewall or VPN, can you set up a different user on your phone? - and be disciplined in is use.