I don’t know about that specific browser. But there is something similar in use in schools here. Basically they know when you’re leaving the browser window ( e.g.: to open a text file or a different browser ). Other features probably are that they can monitor you through your webcam and/or listen to your audio as you are making the test. The reason is so you don’t have somebody under your desk reading you the answers. Or you don’t have your course book open while making the exam.
The school could honestly provide the alternative to go make the tests in the school itself under supervision on paper or on a school device.
It’s a secure anti-cheating browser, not a secure privacy/anonimity/hardened browser.
It’s not meant for day-to-day use. Only for making the exams.
You can always get a secondary cheapo device purely for the exams ( or an old laptop).
If just one or those passwords gets leaked you might find a lot of other ones get cracked as well.
It may not be sites that you care about. But using a password manager is a lot less effort and a lot safer than whatever technique the average Joe will come up with.
Any password that leaks which could indicate a potential system ( e.g.: sitename in lower/upper/leetspeak) makes the whole thing even more vulnerable.
Just use something. Bitwarden, vault warden, keepassxc, …
Knowing my social circle I’d recommend bitwarden. Even paying for it costs a measly 10$/year, while the free version is very usable in itself. And generating passphrases or 32char passwords will be a lot safer than whatever the hell they can come up with.
Just avoid the default browser ones, big tech and LastPass.