As of September 8th, 2021, many of the original review actions added back to the new review queues, including voting on the post or comments, flagging, and commenting, accompanied by the button "other action" to complete the review.
As you are probably aware, this change is due to the latest changes in the review process.
I'll first try to explain how this new system forces reviewers to leave these often irrelevant comments, and then say what I think must be done to improve the situation.
By my reckoning, the reviewer who left those comments (i.e. the person behind the Community♦ user) did so because this is the only way you can "complete" a review. Previously, if I recall correctly, in the review process for first questions and first answers, there were two options to finish the review and move on to the next one, "nothing to do" for when the question/answer is fine as is, and "I'm done" for when you're done performing some kind of "review actions". Review actions in the old review queue include voting on the post, voting on existing comments, commenting, editing, and flagging. Doing any of these will activate the "I'm done" button, but you can perform all the review actions you feel necessary before clicking on the button to finish.
In the new first questions queue, the "I'm done" option is gone, and in order to complete the review, you have to choose from three options, "looks good", "edit", or "share feedback". This means that if the question is not up to the standards of Math.SE, you'll need to either edit it, or "share feedback", while flagging, voting, and voting on comments are no longer "review actions", making it impossible to complete a review with these actions. In other words, even if you voted or flagged, the review system would behave as if you've done nothing, forcing you to choose one of the set options, or skip. Moreover, the only way a comment can complete a review is through the "share feedback" button, and you have to choose between the canned feedbacks. A custom comment made under your own user name is also treated as if you've done nothing. Also noteworthy is that you can only perform one review action at a time, so if you edited a question, you cannot also share a canned feedback.
Thus reviewers are presented with a dilemma (cue the sweating in front of two big red buttons meme), when reviewing a question that needs more work do they follow the new SE procedure, or do they try to improve the question following Math.SE conventions? If they choose to stick to the workflow of the new review queue and the best action in their opinion isn't provided, besides flagging/voting/commenting or doing whatever they see fit anyway, they would also have to either (1) make edits (which doesn't address questions that lack context, since only the OP is able to provide it), (2) leave canned feedback (which can be irrelevant as you pointed out), or (3) click "looks okay" (but the question is decidedly not okay, and now this might skew whatever metrics SE uses to decide on the quality of contributions). Right now the two workflows are in conflict, and so far, the only way I've found to kind of follow both is to review as I would in the old review queue system, then skip the question. Note that this is an imperfect solution (as is not doing reviews at all) to the problem you raised, because if a review is skipped, it will just move on to the next person who might take one of the more imperfect options.
Note that this problem may be resolved soon, because after many bug reports and feature requests, SE has decided to make some changes. In the list of changes,
Reviewers will be able to create their own custom feedback through the Share Feedback modal. This custom feedback can only be shared as the reviewer themself, not the Community user.
Mods will be able to delete Community bot comments, and other users will be able to flag the comments as "No longer needed."
will, I believe, mostly solve the reviewer's conundrum, since they will be able to leave, for example, this (already well-used) comment from the List of comment template meta thread, which also satisfies the three points you listed,
Welcome to [math.se] SE. Take a [tour]. You'll find that simple "Here's the statement of my question, solve it for me" posts will be poorly received. What is better is for you to add context (with an ): What you understand about the problem, what you've tried so far, *etc.*; something both to show you are part of the learning experience and to help us guide you to the appropriate help. You can consult [this link](https://math.meta.stackexchange.com/q/9959) for further guidance.
In my opinion, however, it would be better still if the canned feedback were per-site configurable, because then it would be possible to achieve a community consensus on what the most productive thing to say is. Unfortunately, SE staff say that "this is a fairly large undertaking that we're not flat-out declining, we just don't have the resources to get to it right now." So my hopes of this getting implemented in the near term are not very high.
Additionally, as to the problems of not being able to perform multiple review actions and many previous review actions not counting anymore, there might be upcoming changes to solve them. A feature request asking to bring back the "I'm done" button is labeled "status-planned" and worked on right now by SE staff. Therefore we can expect some update soon to that end. Hopefully, this will allow for multi-action reviews and bring back flagging and voting as options to finish a review.