In this context, I feel it's OK for GP to remove their blog or Mastodon posts - not weird at all. However, I believe I am well within my rights to scrap GP's blog, screenshot all their Mastodon posts, and keep them for reference; I'd expect the blog to be indexed by the Internet Archive, and would find attempts at preventing the IA from making a copy as something between peculiar and antisocial.
That is, there's a distinction between owning the message itself, vs. owning its physical form or means of publishing. The former, I believe, is always shared between sender and recipient or recipients (up to and including everyone, if we're talking about a regular website without any access control). The latter is handled through normal property law mechanisms, but owning the medium only means you can decide who can access the message on/through that medium, not that you own the message itself.
Why not discord messages then?
But that's more of a forum or a publication than an interpersonal communication. I think when you and I talk, we both own the content. The conversation is two-way, and thus it is ours. You have no right to take those conversations from my email server any more than removing them from my mind.
It's not about one-to-one or one-to-many, it's about is the conversation one-way or two-way. Are you talking to someone or with them?