I was waitlisted las year
Sent at least one email every 3-4 weeks.
After being waitlisted I:
visited the school, visited my waitlista manager, attended a class, attended admissions event ( sent a thank you note explicitly everything). Not sure if a option due to covid, but I guess you could do something similar 1st update.
got an supportive email from one current student . 2nd update
-I was approved in another school with $$. I let cbs know and reiterated they were my top school. 3rd update
Finally, wrapped with a big thank you note, I did everything I could, thanks for the opportunity. 5th update.
I did that in a few months, 2 or 3. I guess you have less time, but I don't think giving meaningful updates for admissions could hurt you in any way.