I had 2 pregnancies, first was natural, second I got induced at 39+ even though cervix still closed.
I was worried too, but my gynae did cervical ripening first, then started labour. Took some time (almost a day), but I still delivered vaginally, no issues.
From what I understand, quite common for second pregnancy to need a bit of “help” even if first was smooth. If your gynae recommends it, usually means it’s considered safe.
Maybe just check what method they’ll use and how long they’ll wait. I felt the same anxiety before, but turned out okay for me.