@nbianca identified that this was caused by an experimental theme component we had running on Meta, and only affected the composer preview.
I disabled it, and it works now:
<h1>test</h1> *test*
<h1>test</h1> :)
test
*test*test
:)As for the original query, <h3>hi</h3> :smile: is rendering in line with the commonmark spec
