This is a thing on the PS5. You cant just browse the web like the PS4. But you can open links in messages. So put https://google.com in a message and open it

wow, mind blown at this ps5 "detail" yuk

Why bother, you can use a pihole/etc and redirect the users guide to wherever you want, like a webkit exploit and hen enabler. (Which is what they've been doing since the ps3)

This is used for homebrew. There is (of course) a WebKit exploit on some firmwares and there is a way to get arbitrary page load by going into the help section then bouncing around in several Google help pages until you get to a search box, search for the exploit page and click it.

My school (where I work) seems to be blocking certain SSL certificates or blocking at the DNS level but changing the DNS server to 1.1.1.1 is futile. Using Mullvad’s free DoH or DoT is futile as well. The website is unable to load

The VPN is one of the few reasons why I pay $5 for proton unlimited and I could make do without it.

My only alternative is to set up my own wireguard exit node at home with a raspberry

Your school is likely using a NGFW like a Palo Alto. These provide very granular application based filtering of traffic.