I don't believe a public institution would be able to come up with a system like this that works reasonably and have it developed in a reasonable amount of time within a reasonable budget.
I don't believe “e-proctoring” companies are capable of it, either. I got disqualified from an exam for five `onblur` events (while my screen was being recorded), and it kept counting while the “DO NOT CHEAT” lockout message was displayed; if that's “works reasonably” then I don't know what isn't.
We spent 6 months on it and as far as I heard was still in use as late as 2015.
You don't have to create a whole system; just a database that prepares variants of questions, and a method to put it into the existing exam software.