Work computers are for work, and pretty much every employer monitors what you do on it.
Depends heavily on where you work. My employer don’t track what we use the computers for (of course there’s a ‘TOS’ of sorts which says that it’s company property and should only be used for company stuff) but as long as you are at least somewhat reasonable on what you use the system for it’s fair play. Things like checking your personal email and occasional visit to lemmy/whatever your social media poison is doesn’t raise any flags as long as you get the job done and that’s it. Of course you can’t install anything on the system but as long as a browser session on incognito mode is enough and it doesn’t harm your duties, while technically forbidden, no one really cares.
And yes, I know this for sure, as I’m one of the guys who enforces the policies for our gear. YMMV.