People really should use more than one browser or profiles within the same browser, so that even if something malicious sneaks into their browser, it wouldn't be able to steal cookies, logins and execute attacks against important sites. So, you could use Chrome for reading news or visiting entertainment sites, but then have Firefox for checking your main email, doing banking stuff and crypto. This doesn't mean that you can become careless when you use multiple browsers, but generally security by isolation is much stronger than relying on user to not let malware into their system.
You're referring to containers which do provide a way of dissociating browser data via placing them in containers. However, it does not protect you from all kinds of attacks. A website could theoretically target users with containers, and find the linked data. Another misconception is browser containers prevent malicious software from spreading, but this is also not true. Using separate browsers does the same as containers, but also prevents to a certain extent websites linking your agents together. Although, this isn't the best option either. You can spoof user agents, use script less browsers, and block trackers, but you have to do this in such a way that no third parties are involved. As soon as you involve a third party such as a closed source extension you are at risk of giving your data to the extension owners.
Security by isolation, or compartmentalization is only possible via utilizing virtualization technology at a BIOS level. If you are isolating via virtual machines on a "ordinary" operating system you're not isolating effectively. Virtual machines such as VMware, and virtualbox do offer some protection, but not entirely. This is because they are not operating at a base level, and don't use their own hypervisor.
I've talked about this recently a lot, but I'd recommend Qubes OS for effectively isolating your machine. There are alternatives, but my personal opinion is Qubes OS is the most effective one out there. This truly isolates every domain separately from the other. The only way the whole system is compromised is if the Dom0 (the root of Qubes OS) is compromised, but you should not be doing anything on DOM0 except for updating for critical exploits. I wouldn't even have DOM0 connected to the internet, but Qubes OS allows you to create different domains (workspaces) for whatever you want. If you want your network to operate on a VM separate to the rest of your computer you can, and that is 100% recommended.
Does it have to be Chrome, or would they accept Chromium based browsers? On the rare occasion I have a need for a Chromium based browser, I always use
Ungoogled Chromium.
They unnecessarily marked assignments to the letter. If it says Google chrome developer console you better be using Google chrome console otherwise you could potentially be marked down. This is likely due to it being distance learning, and you're compromising because the lecturers aren't full time, however was necessary to me because I couldn't justify giving up work to study so opted to do both with distance learning.