The right of first refusal is the publisher's, not the author's. Really. See
this. Or
this. (Quoting from the latter, "In layman’s terms a right of first refusal gives the publisher the right to bind you to them for your future projects.")
Right of first
offer (which the author could refuse) is a different thing, but not what is at issue here, btw. If the publisher retains right of first refusal, it is keeping
for itself that right (first opportunity to say "no" to the author's next book).
Also, see
this, which outlines some variations on the theme with different implications for the author. But as for its view of right of first refusal, "Today most attorney-written contracts give the original publisher an option on the author’s next book, and sometimes on the next several books. Some such clauses specify that the next several books will be published on the same terms as the first book."
Hence my (nonlawyerly) recommendation to make sure that next submitted mansuscript is a throwaway, sufficient to pass a bare test of credibility (not gibberish, not only a couple of pages, etc.), but of no real value to the author.
At some point, one of the authorities here will chime in.
--Ken