Chrome will now mute notifications by default when it detects you're sharing your screen. It should be hitting all accounts soon, but you can manually enable it now if you'd like.
The feature is very straightforward; it'll simply hide the contents of incoming Chrome and Google Chat notifications if one comes in while you're sharing your screen. Google already muted notifications when sharing a tab in Google Meet, but this will now work regardless of how you're sharing your screen.
This is rolling out now, and it should reach virtually all G Suite users within the next three days. If, however, you want to try it out now, you can manually do so by enabling it in flags (chrome://flags/#mute-notifications-during-screen-share).