Counterpoint: look at your screen. Is there anything there that would cause a problem if you shared? Why is it there? What if someone looked over your shoulder? What if you accidentally shared?
Develop the habit of recognizing and removing or even entirely isolating sensitive info unless it is the active subject of your attention. Your safest bet is to ensure a data leak can't happen even if people do see more than they should.
@Biggles so ... nobody should work on non-public projects, or on work for multiple clients where you can't disclose client identities?? It's entirely reasonable to be working on private or secret projects on your machine, and still need to present to other people from that same machine; we don't all operate out of a SCIF. Taking steps to mitigate potential risk (like I outlined in the OP) is just good practice; telling people "you should never do anything where you might potentially expose sensitive information" is not very helpful.
"Look at your screen". I said nothing about what you are doing, just about what is showing. The first step in ensuring nobody sees something they shouldn't see is to close the damn window - don't count on your screen sharing preferences to protect you. Defense in depth. Make is so that *if* you accidentally minimize a window or switch tabs, there isn't something there to care about. I didn't say "you should never do anything where you might potentially expose sensitive information". I said clean your room before mom gets home. Before you join that call - look at your screen and maybe close that password manager, or client list - just in case. Even if you aren't presenting, because - you might be, and accidents happen.
Using a new window doesn't eliminate the failure mode - you're one typo or click away from exposure. Bookmarking your tabs (i *absolutely love* the One Tab extension) and closing the window makes accidental exposure a multiple-mistake process.
The bookmark menu is an easy fix - use folders. So even if it drops down - no worries. I can open my work browser in front of you and the most sensitive bit of info you'll see is the name of my employer.
Caveat: I'm super paranoid. My focus is and has been security, for a while now, and I often have things up that would be bad for others to see - IAM and security audit findings. I look at things and say 'how does that accidentally get compromised". It drives my wife *absolute nuts*, because outside of work it's a bit of overkill. But - security is a habit or it fails.