So isn’t Puijila darwini the common ancestor for Pinnipedia and Musteloidea only? After they split off from Arctoidea? And the bear-like ancestor would be Arctoidea being as it includes Ursoidea as well?

No. Puijila is basal to Pinnipedia, but since it looks like an otter, Puijila clearly shares a common ancestor with Musteloids, so I’m not sure where this “bear-like” ancestor is supposed to fit in. All of Arctoidea likely has a bear-like ancestor (wolverines, which are in Mustelidae, retain remarkably bear like features) but to say that is obviously very different than saying Pinnipedia alone.