This answer posted by Shog9 lists how a post becomes a Hot Meta post: What criteria are used to select the links that appear in the community bulletin sidebar block? (current revision). Among the conditions listed there, it says that a post tagged with a moderator status tag will not become a hot meta post. But the tag featured isn't mentioned there.
Question: Does the featured tag prevent a post from becoming a Hot Meta Post?
I can imagine that the developers might have decided to do this - in order to prevent a post from appearing in the community bulletin twice (once as a featured post and a second time as a hot meta post). But if it is the case, probably it would be nice to include this information in the post documenting how the hot meta posts (and the community bulletin) works. (Of course, the other possibility could be to give the post "hot" status - but when selecting entries into the community bulletin, check that no post appears there twice.)
Recently there was this post on MathOverflow Meta: Upcoming election announcement (2022). Neither the timeline nor the revision history list it as a hot meta post. As far as I can tell, it fulfills the criteria described in the current revision of the linked answer.
Using a SEDE query, I found three posts on Meta Stack Overflow that are both featured and, at the same time, the posthistory includes becoming a hot post. And one of them was first tagged featured and then became a hot meta post. (So in that particular instance, this tag did not prevent the post from becoming hot.) At the moment, I do not have time to create a networkwide query searching for similar things on all per-site-metas. The linked query only shows the posts which have the featured in SEDE at the moment - maybe including a similar query for posts which had such tag in the past could be interesting, too.
Here is another recent instance of a question on Meta Stack Overflow which became a hot meta post while it was tagged (featured).