Teams pinging my phone while I'm sitting at my desktop

Teams on the phone: tap your picture > Notifications, there's an option to block notifications when active on desktop. Turn that on. It relies on the desktop app seeing you as Available, after a few minutes of no mouse movement it marks you Away and the phone starts buzzing again, so a long meeting or a read-only task will still ping. Separately, under the same screen you can set quiet hours.