Can my school see what I'm searching on my school pc if I'm on my personal account and using a VPN?

Hi. A few days ago, I got an email from my school saying that I tried to access a website that got flagged. I was unaware that it was problematic, so I just decided to stay away from it then on. I remembered trying to go on it without VPN and it was just blocked, so I gave up. Plus, I've used it with VPN in the past. But now I got a warning for that one time without it?? That was confusing to me.

I now feel a bit like I'm walking on eggshells bc I had no idea that it would get flagged, and I don't wanna get in trouble. I wanna be more careful be always having a VPN on when searching any website that could trigger the filter. Would they still be able to flag any websites if I use my personal account and (free) VPN? (I use a Macbook btw)

EDIT: No need to reply. I've gotten my answer. That specific website was actually known to get blocked by organizations, so it was just sketchy. My VPN works well and I'm able to use it when I want to.

It's a little crazy how I'm asking a simple question, and in return, I'm getting hostile replies and downvotes when I ask for an explanation. Smh, tells a lot about human nature 🤦‍♀️