Recently, there have been a couple of active questions on Publons (e.g., Publons - is it a serious thing? and Is it worth creating a profile with Publons?). One of the supposed selling points is that it allows people evaluating you to verify the peer review work you've done. At least one user says your peer-reviewing is one criterion used for promotion.
I am in pure math at a public research university in the US, somewhat senior, and I don't recall ever having seen any real discussion of a job/tenure/promotion candidate's peer-reviewing activities in the evaluation process. It is a given that you do some refereeing, and it counts as part of your service to the community, but unless you state that you do an exceptional amount of refereeing or consistently referee for the very top journals, I probably won't even notice your reviewing activities. If I do notice, I will quickly forget. (I don't list the journals I review for or how many reviews I do on my CV, and I believe this is reasonably common in math. So I wouldn't even know if someone I'm evaluating isn't doing any reviewing.)
However, the nature and expectations for peer review for pure math seems to be quite a bit different from other fields.
Question: Are there departments that, say for hiring, tenure or promition, use candidate's peer-reviewing activities in a signficant way in the evaluation process? If so, what kind of departments use this and how?
(While "significant" may be somewhat hard to pin down, two examples are: peer reviewing regularly gets discussed when evaluating candidates, or if there is some formula for numerically scoring faculty which incorporates peer-reviewing activities.)