Right now James F. is still the product owner of the concept of Wikimedia having Beta Features in production, dating from when he was product owner of all contributor-facing features.
The primary work is helping teams go through the process, on average around once a year, and reminding teams with live features that they need to either ship or shut down (nominally, within six months of their last major feature change; in practice, it can go longer during e.g. a staggered roll-out).
The principal product objective is to help teams provide a great experience for logged-in users without overwhelming them with too many features at once, and reducing cognitive complexity for how different wikis might be.
This shouldn't be owned by a person so much as a position, and it should definitely be owned by an actual product person – possibly @MMiller_WMF?