By R&R, you're referring to revise and resubmit right.
We all know that reviewers can be very subjective, and they may or may not agree with the initial reports.
Reviewers ought not be subjective. Unfortunately, it happens. Sometimes, some are just 'pedantic' regarding methodology and/or methods. Nonetheless, reviewers are not compelled to agree with the initial reports.
I wonder if it is even ethical for journal editors to invite an author to revise and resubmit according to some comments ...
Handling Editors are free to invite new or additional reviewers even during R&R. I've had manuscripts sent my way for review, and I can see that the manuscript is at the second or third review stage. For such, I have the liberty of seeing and deferring to comments from earlier rounds. However, I normally review as if I'm the reviewer of the first instance. When I'm done, I then check earlier comments.
In summary, there's nothing unethical about inviting new reviewers for R&R. Having said that, I know that most handling editors will invite earlier reviewers except where the reviewer had clearly indicated non-willingness to review subsequent resubmission of the manuscript.
Or should the second round review be based on the previous comments and the revisions, at least heavily so? Otherwise, it would be more like just another round of review.
As I indicated, the second (or even third) round need not be based on previous comments. The norm, though, at least in the three disciplines I'm into, is not to keep shifting the goalpost. A reviewer should read through the manuscript thoroughly and comment appropriately. It is out of place for a reviewer to keep raising new 'issues' at each R&R rounds. Where there was an oversight initially, nothing preclude the reviewer from apologising and raising them. Just not the norm.
In any case, the interest should be advancing/contributing to the body of knowledge and ensuring quality articles.
What do journal editors usually do in this kind of case?
Simply put, in my own experience, the unavailability or inability or unwillingness of previous reviewers.