> Anything you do with the company property, e.g., work computer, automatically belongs to the company, even if you do it on the weekends. That doesn't sound unacceptable to me. It's not that I'm that strict about e.g. reading personal emails etc. on my work computer, but if it's some side hustle, be it for money or for fun, I think it's honest to take your personal machine for that.
Computers are just office equipment, just like pens. If I gave you a pen and you wrote some story with it, then could I claim the rights to that story? I think not.
More seriously though, there are frequently restictions of the use of office equipment (or business equipment in general). Businesses will often overlook it if it is not a problem, say if you need a photocopy of a rental contract. They have the discretion to say no if the privilege is being abused, say if you started printing hundreds of pages a month for personal use. The misuse of pens is rarely seen as an issue since they hold little intrinsic value and are routinely replaced.
Should they be able to claim the rights to something you produced with their equipment? In most cases, no. I'm not going to say in all cases no since there is always going to be someone who pushes the limits beyond reason. (Say a person develops a piece of software with a company computer to sell on the side. Can that be construed as the business indirectly financing the development of the software by providing hardware and/or software tools?)
In general, it is always a good idea to do personal stuff with personal equipment and business stuff with equipment supplied by the business. I'm sure the coworkers who are searching for the missing pens will thank you for doing so.