I think the "not recognized as work" part feels similar to my experience but I don't really understand the psychology of it. Work is not done until it is reviewed and merged, so the review part is necessarily a part of the work cycle. I don't get the sense that you're advocating for the "not recognized as work" perspective, just responding to that viewpoint you shared.
I feel sorry for you working in such an environment, that really sucks.
I have received praise for my review, I have had it mentioned by my manager, including in performance reviews, I have thankfully had leadership emphasise to everyone on the team how much it matters, and I've had great retrospectives on how we can improve the quality and speed of review that resulted in further meaningful improvements.
Changing culture on this is hard, so maybe the answer is just to find a better culture elsewhere, but I can assure you that it does exist.
if your reward system isn't based solely on your performance review, but rather than the speed and quality in which your project is completed, the respect of your peers, and their willingness to engage with you in kind, then absolutely being a timely and considerate reviewer is rewarded.
Nobody has ever praised me or (as far as I know) a colleague for reviewing work. Certainly not a manager.
My reviewing doesn't show up in Jira under the amount of work I completed.
No performance review of mine has ever mentioned reviewing code.
In summary, there is minimal credit to be had from doing the work and even when there is credit, nobody lets you exchange that credit for much.
Yes, by rule reviewing is considered work, but it is not work anyone gives you much credit for doing. As an individual with incentives not aligned with the company most of the time, that makes it not worth prioritizing.
So I suppose it is recognized as work, but it is the least rewarded of the work you could be doing.