Hi all,
I moved within canton ZH, so following these instructions I notified online my new address to Strassenverkehrsamt. Then it says to send them the original car papers so they can change the address there.

My doubt is: can I still drive around while I don't have the car papers? What happens if I get stopped?

Thanks

Photocopy them and keep that wth you while you are waiting for the new papers.

As the others said. However do not drive abroad until you get it back. (Not much of an issue in these days, I mean going abroad as the borders are mostly closed).

or just stop by the Strassenverkehrsamt and have it done in person in 5min

It will be surprisingly quick, a few days at most. And every policeman has heard the story numerous times.