Is it appropriate for peer-reviewer to look for possible plagiarism?
I would immediately communicate your findings to the editor and do no further reviewing until you hear back from them.
In the best case, like you say, they forgot to edit it, and can resubmit. Communicating to the editor will let them stop the other reviewers so they don't waste their time either.
In the worst case, it's poorly executed plagiarism and you would have to contact the editor anyway.
To answer the title question, of course there's no issue looking for plagiarism, and you seem familiar enough with the field to understand the implications of your results.