What "no WiFi needed" actually means
Cameras sold as needing no WiFi record to a memory card inside the camera. That is genuinely all they do. There is no live view, no alert on your phone, and no way to see anything without walking out to the building, taking the card out and putting it in something that can read it.
For a trail camera watching for deer, that is fine — you collect the card when you are out there anyway. For a barn, it usually is not what people wanted. The reason you want a camera on the barn is normally to see the barn without going to the barn.
The distinction that matters
A camera needs a network connection, not an internet connection. Those are different things, and conflating them is why this search happens at all.
Once the building is on your network — by any means — cameras there behave exactly like cameras on the house. Live view, alerts, recording to a box in the house, remote access from your phone. The camera does not know or care how the network got there.
How the network gets to the barn
The usual answer is a point-to-point wireless link: two small radios, one at the house and one at the barn, aimed at each other. With line of sight between them they carry a full connection across distances a WiFi extender cannot usefully cross. No trenching, and it goes up in a day.
Where there is no line of sight — a stand of trees, a rise in the ground, another building in the way — buried cable is the alternative. It is more work and more money, but it is unaffected by weather and does not care about the canopy filling in come June.
What does not work, reliably, is chaining WiFi extenders across a yard. Each one halves throughput and needs a decent signal to begin with, so by the third hop there is nothing useful left.
When the card-only camera is right
There is a real case for it: a remote corner of the property, no power, nothing to link to, and you genuinely only need to review footage occasionally. A battery-and-card camera is the correct tool there and nothing else would be better.
The mistake is buying one for a barn two hundred feet from a house that already has a fast connection, because the search results pushed you that way.