How can I see when a phone is on dnd

No longer the case in iOS 15. If you turn on the “Share Focus status” option for any particular Focus (including Do Not Disturb, which is now a type of Focus) it will share your status if people message you. It won’t share the name of your Focus, just says your notifications are off. (You can only choose this option if you also choose to share your Focus status with all of your devices.). You’ll only see a notification like that from other people if they’re using iOS 15 and have chosen to share their Focus status.

The only time people can actually tell when you are on DND is when you use DND While Driving, it sends an automatic message.