Is it true that many famous tech people like Mark Zuckerberg cover their laptop camera with a tape

Yes: Mark Zuckerberg puts tape over his laptop cam; you should do the same

The key qualifying word here though is “famous”. If you’re not famous, there’s little point in that:

• There is surprisingly little useful information that could be obtained from a camera hack. For what I care, people could stare at my fat ugly face (or the wall behind it, if I’m not at my desk) for as long as they want. Sure, if I’d be Zuck, my mugshot could be worth something, otherwise meh.
• A microphone hack would be significantly more dangerous, as it would provide a helluva lot of business context. Given the sensitivity of todays’ devices though, I doubt that a tape could actually protect you.
• Whoever has access to your cam and mic, would probably be able to take screenshots or, worse, install a keylogger on your laptop. Those are “game over” situations, and there’s no place on the laptop you could stick a tape to prevent that.
• It may give you a false sense of security, and an unwarranted peace of mind. You shouldn’t have that. Worry about not letting people access your camera, rather than blocking what they could see.

TL;DR: unless you’re famous, don’t bother. It won’t do much for your security.

Stay safe!