If you look at the community-bulletin tag info, you can find a link to this post: What criteria are used to select the links that appear in the community bulletin sidebar block? on Meta Stack Exchange. The post describes in detail, how a question gets into the community bulletin.
In short, only the questions from past two weeks, only questions having the discussion tag and score $\ge3$ are selected. The mods can use the featured to add something to the community bulletin - although the question is then shown as "Featured on meta" and not among the "Hot meta posts".
But it seems that SE is considering including also the questions with the feature-request tag. In fact, changes related to this caused a bug which was reported quite recently, see: New questions are not being added to the community bulletin (on Mathematics Meta), Only meta questions with both [feature-request] and [discussion] meta tags are featured in Hot Meta Posts (on Meta Stack Exchange) and Feature non-[discussion] meta post in the community bulletin (on Meta Stack Overflow).
Looking at the current criteria:
- The question "Proposing a change to the close-vote interface" does not qualify - it does not have the discussion tag.
- Proposing a change to the close-vote interface fulfills these criteria - but the third upvote was added only recently. You can see on the timeline and in the revisions history the event saying "Became Hot Meta Post" together with a timestamp. Since it now has score $+3$, it should is among candidates for hot meta questions and it can be randomly chosen as such. (Unless somebody downvotes it and the score falls below $+3$ again.)
Becoming a hot meta post is shown in the history only since August 2020. (See: Recent feature changes to Stack Exchange and Hot Meta Posts: Allow for removal by moderators, and thoughts about future improvements.) This means that you can get them from SEDE using similar queries as for the Hot Network Questions. For example, here is one such query. (The same query was mentioned also in the chatroom listing bounties and HNQs from MO.)
Using SEDE you can also see which questions had the (featured) tag in the past. It seems that, among the current moderators François G. Dorais uses the tag most frequently.