The word is autoembeds work for padlet.com links- a wee test here for
https://padlet.com/cogdogblog/aos9fosbbwk4 if I just paste in this address to the editor, what happens?
Yup! It works. It could not possibly embed any other way here beyond it being supported.
Now why do they not let people at WordPress.com know? And why is it not enabled this in sites powered by WordPress.org? I figured out on my self-hosted site how to add Padlet as an oembed provider despite there being zero documentation it was possible.
Did you see what I did there? A link from giphy.com is also auto-embedded in a WordPress.com site.