Yes, these questions should be on-topic as they satisfy the constraints of the specific reference tag that the solutions manual are a "short, non-open-ended list of resources". Either the book exists (and is publicly available) or it doesn't exist (or isn't publicly available). Answers would either provide the link (which is a suitable answer, as mentioned explicitly in the tag info) or state that no such manual exists.
We also have a mod indicating in one of the posts in question that
...this is a good use of the specific-reference tag. At least, it is among the type of question the tag is meant for. It could still be considered off topic, though; we'll see what others think.
Which seems to indicate that such questions should fall under the specific reference tag and, since no one raised the point for over 2.5 years, the community seems to have implicitly assumed the position that everything is fine.