In the article they state "We found that emojis were sent in portal messages to patients aged 70 to 79 years at the second highest rate, after those aged 10 to 19 years" which implies some of this at least is in messages to patients.

I can see sending emojis as a way of trying to be friendly and informal in communications with patients, especially if the patients have already used them.

Patients are all different so I can see some of them hating their use, but I can also see some patients appreciating a more lighthearted tone.

Pediatrics in particular is full of this kind of stuff in general.