I am British and live in England and have no idea what “you’re a chip off the old block” means even though I’ve heard people say it before (but not that often).
やっぱり親子ですね to me looks like it should be translated as something like, “After all, you are your parent’s child” which is maybe what the chip off the block expression means (you are a product of your upbringing? You’re just like everyone else where you came from?). It just seems strange to be translated into some obscure British expression which doesn’t mention parent/child even though those are the kanji used. Could やっぱり親子ですね be translated as “after all, you are your parent’s child”?