Who actually owns Messenger now?

Meta, the same company that owns Facebook, Instagram and WhatsApp. Messenger started as Facebook's built-in chat and got split into its own app in 2014. Facebook rebranded to Meta in 2021, so it is all under that umbrella now.

If it is account related, turning on two factor while you are in there is always worth it.

Older phone here and the permissions reset fixed it, give that a go.

Meta. It has been part of the Facebook/Meta family the whole time, just spun out into a standalone app years ago.