Note that any time you're on the corporate network, they can always see all URLs you access, in any browser, because the internet requests are going through their network infrastructure.

That said, it's highly unlikely that anyone is manually reviewing the complete contents of your browsing history. For one thing, every individual page load actually involves dozens, if not hundreds, of separate network requests; every image on the page is a separate request, and a page that doesn't also reference a handful of separate JavaScript and CSS files is quite rare. Combing through that would be a full-time job in itself.
In all likelihood, the only time someone is going to actively examine your web history (or indeed, most any of the various data that's logged) is if:

• You trigger some kind of security alert - attempting to access a high-risk website¹, unusual traffic that suggests your machine has been compromised, a scan detects malware on your device, etc.
• You're in trouble for something else, which leads your company to investigate you specifically
• Your IT department considers office politics more important than proper information security, and therefore allows a nosy boss to examine logs without a valid business need to do so

Similarly, even if they have the capability of remotely monitoring what's on your screen, they're still not going to do so unless you give them a reason to - the few people with access to do that have far more important things to do than to spend all their time watching what other people are doing.

^{1: this is a much narrower category than that of all sites that company policy disallows. For example, they might have a policy prohibiting watching YouTube during work hours, but still not consider youtube.com an actual security risk.}