When I started university, it did indeed have a dedicated building that was essentially a computer lab specifically for testing. In theory, cheating was prevented by having people walk around the lab watching the students. Toward the end, I did have a couple exams that needed the absolutely batshit insane malware installed on a personal device, but I think if I were to do it again today, I could still demand to use the testing center instead. It still exists.
From my experience, the safeguards only come up during exploit development. You are free to do reverse engineering and even the first half of vulnerability research (i.e. vulnerability discovery) and it only stops once you want it to actually write the exploit.
This post is about the search engine, not the web browser. I use Brave instead of Google search because Google presents me with captchas every time I use it, and Brave's search engine is good enough. I already use Firefox and ublock origin.