I've been writing audio reviews for publication for the past 20 years. I"ve covered both equipment and music. Based on my experience I'll speak to the ad hominem questions first.
Reviewers are hired by publications or editors according to whatever qualifications the publication chooses to adopt. I've written for three publications. None of those had specific qualifications and I believe there are no general or industry wide tests or qualifications for being a reviewer. Each publication has its own set of rules and protocols a reviewer must follow.
If you think there should be formal qualifications to be a reviewer, you can clamor on the internet but to get something like that to happen you really need to direct your views to a specific publication -- an employer. There is no industry-wide organization or council that sets rules for the audio industry.
I was doing rudimentary alpha and beta testing for a friend who worked for a major industry manufacturer and who had been a reviewer for Soundstage. That casual work involved listening to products being considered for production and giving feedback to my friend who passed them to the manufacturer. Both the manufacturer and my friemd found helpful the descriptions that I wrote. It was fun. For over a year my friend encouraged me to write for publication. I kept taking a pass on that but finally he and and someone at Soundstage convinced me to try my hand. If success associates to continued employment, then I've been successful.
As to what counts as 'employment', that means continued publication of one's writing. Unless you are a columnist or in the editorial hierarchy there is little monetary compensation for a reviewer. Reviewers are paid so the publication can own the rights to a review. I can't remember being paid more than $150 for a review. Given the amount of time and work required for a conscientious review, it is clear to me that I'm not doing it for the money.
Being a reviewer for an established publication places you as a participant in the industry. Members include manufacturers, distributors, retailers and the media. It is an unwritten acceptance that as an industry participant a reviewer accrues entitlement to industry accomodation pricing, just like any other member. That is some percentage cost below MSRP as determined by the manufacturer or distributor. This, in my opinion, is the primary compensation a reviewer receives. There are rules governing accomodation purchases set by the manufacture and/or the publication. For example: a reviewer needs to get permission from his publisher to make a purchase. The reviewer is barred from reselling an accomodation purchase for some period, usually 2-3 years.
As to titles or descriptions ("are they critics? reporters? journalists? marketers? cheerleaders? influencers?") -- you tell me. From your list, the closest for me, is reporter.