Is it okay to incorporate a block of citations from a review paper into my own paper?

You must cite your source every time you use someone else's intellectual contributions.

A review article contributes curation of sources (among other things) as its intellectual content. If you use that intellectual content, you must cite the review paper (in addition to the individual sources). Otherwise you are misleading the reader into believing that you've done all that work (reading very broadly in the literature, identifying the most relevant and useful sources) yourself.

I do not see why that would be plagiarism at all. Taking references from other papers, reading them, and citing them in your own paper is a regular process. If you copy & paste the sentences that refer to those citations along with the references, then it would be considered plagiarism, but no, not in your case.

Perhaps your choice of the word "steal" to describe the inclusions of block citations reveals your feelings on the matter.

If you are copying text verbatim, and I assume it is by saying "block of citations," then you should provide a citation to the source. That is my take.

However, by altering your conundrum slightly, does it lead you to a difficult question or an unknown? As in, had you found these papers 12 months ago and the question of copying the citation block wasn't applicable, would you have cited the paper in which you discovered these additional sources?