TL;DR: Should the tags peano-arithmetic and theories-of-arithmetic be merged? Is some clean-up needed before doing that? Or are there some reasons not to merge these tags?
In October 2020, a tag synonym peano-arithmetic $\to$ theories-of-arithmetic was created as a result of this discussion: Creating theories-of-arithmetic logic tag However, the two tags have never been merged.1
On one hand, I understand that merging tags should be used carefully - since the process cannot be reversed. At the same time, leaving the two tags in this state means that some questions tagged peano-arithmetic will not be returned in various searches.2 The issues with searching were mentioned also in jeq's comment to the answer posted by the moderator who created the synonym.
Since these two tags were synonymized based on the consensus of the community (see the voting in the linked thread) - it does not seem very likely that the synonyms might be cancelled. (Of course, if there is a realistic possibility that the synonym might be cancelled at some point, it would be better to postpone merging. If the two tags are merged, reverting to the original state would mean a lot of manual retagging.) EDIT: Comments posted by Joel David Hamkins suggest that there is some opposition to the synonym between these two tags - and, consequently, if the synonym should be cancelled, merging does not make sense either.
1You can find the questions tagged peano-arithmetic using this SEDE query. (At the moment it returns 195 results.) And you can check that the tag peano-arithmetic is indeed shown on those questions. This means that the tags have not been merged. You can also see that the tag theories-of-arithmetic shows different number of question on the active tab and on the newest tab. (At the moment, 326 and 131 questions.) If you want to see other synonyms which have not been merged, you can try this SEDE query. But I should point out that this includes the synonyms for deprecated tags - where merging would cause more harm than good; considering that those tags have never been cleaned-up. See also: What to do with the synonyms for the deprecated tags?
2It is not clear to me whether this is considered a bug or whether it is intentional. Some related posts: How to find a question by its old tag when that tag is synonymized with another, Tag synonyms and searching and What are differences between synonyms with and without merging from the practical point of view?
3To illustrate this, we might use this question: Iterated Gentzen: or, a Sith objection to the proof of consistency of PA. This question is tagged peano-arithmetic. (In chat you can also see what were the tags at the time of posting this question.) It is among the search results if you search just using a combination of tags. And the search using keywords and tags works if you use some tag which is not a synonym like here. But if you use the tag peano-arithmetic or the tag theories-of-arithmetic, this question is no longer among the results.