I’ve never understood why people ever feel the need to point out whether a pun is intended or not. I never see (rhyme intended) for example, so why puns? To me it tends to disrupt the flow of the prose

It really means, "I didn't originally intend the pun, but now I'm running with it and proudly announcing it to the world." That phrase would be even more disruptive.

It's joke explaining to a broader audience. Tell a joke that's too subtle, only a few find it funny. Call attention to it and more will understand, but those who found it funny as subtle, no longer will.

I think it's bad style. You don't lose anything by people missing your joke. But you risk being viewed as vain and unfunny by cueing people to laugh whenever you think you're clever.