You can run at least an amp over Ethernet cable. A camera probably uses two twisted pairs out of four. No reason why you can’t cut the wallwart cable and connect the wart at one end of the Ethernet cable with the barrel connector at the camera end. Use one twisted pair in parallel for +, the other for -.

Smart TVs with cameras will have limited use, since they’re generally not in all rooms, nor optimally placed to get a good view of an entire room. Plus, unless they support local recording, I’m not trusting the TV maker’s kloudkrap infrastructure to keep footage of my home private.