On behalf of zbMATH (which is certainly also the case for MathSciNet), we would very much appreciate a notification of such cases, if they have not yet been detected at the level of editors or reviewers. There is the general impression of our editors (which has been discussed with our MathSciNet colleagues who seem to share this) that this behaviour has become significantly more widespread recently, and that such papers make it frequently into journals which usually have shown a level of decent peer review (which should generally filter such submissions).
The notification could either be done by an email to firstname.lastname@example.org or to volunteer to write a short review about this case https://zbmath.org/become-a-reviewer/.
We would then evaluate the level of copying and
1) Inform the editorial board,
2) our colleagues of MathSciNet,
3) Add a review or editorial remark mentioning the degree of overlap, ideally taking into account statements of the editorial board and, possibly, the author(s) if provided.
We do not display automated warnings like on arXiv because all existing tools (known to us) produce too many false positives when applied to math content, which seem unsatisfactory for public statements (e.g., arXiv claims overlap for arXiv:1609.02231 and arXiv:1412.0555 where the same problem is considered for genus three and even genus).
Searching for "plagiarism" will not result in all cases, because that means that intention and priority has been clearly identified, which is not always clear especially when things are under investigation (indeed, we had various cases where the paper which was published, or even submitted, first turned out to be a copy of ongoing unpublished other work published later). Hence, the documents will be usually labeled as "identical", "almost identical", "parts are almost identical" etc. - the results https://zbmath.org/?t=&s=0&q=%28%28%22reviewer%27s+remark%22%7C+%22editorial+remark%22%29+%26+%28identical+%7C+plagiarism%29 may give an impression.
Olaf Teschke, Managing Editor, zbMATH