How is it that the Favored Skills like with Barding Gifted Senses

Favorite Skill: Search which is based on Wits (which is the poorest Attribute...

this does not make sense, or does it, is there something I missed?

...and with Distinctive Features on a Barding, Dragon-Eyed
would not Lordly be one of them.

The skills are designed to reflect the overall idea of the background. I don't have the books to hand, so I don't know exactly what Gifted Senses states, but based on the title I would assume Search is pertinent. In regards to the Lordly Trait, I assume that is also to do with the background

It doesn't not make sense.

Having a skill Favored doesn't benefit from having a high Attribute – all skills benefit from that already. Favored skills benefit from a Favored Attribute being higher than the base Attribute.

You get more out of a skill being Favored if the Attribute is 2/5 than if it's 7/8. In the former's case, Favoring a skill gives you a 3 point benefit over what you would get without it being Favored. The latter only gives a 1 point difference.

So the base Attribute is less important to a Favored skill than the Favored Attribute difference – which is chosen by the player.