"to walk something" meaning "to carry something"?

This broadened transitive usage/s 'to walk carrying / carry walking', as opposed to 'to walk wheeling something, or to move something relatively heavy in lurches or at least partial gyrations as you walk':

walk [transitive] walk something: to move a large or heavy object along the ground while walking with it

• He walked the bookcase to the other end of the room.
• We walked our bikes up the hill.

[OALD]

walk [US]{but common in the UK also; EA} 17: to move (a bulky or heavy object) by rocking along from one side or corner to another in a manner suggestive of walking

[Collins]

is becoming more common. Here is an example from Die Trying (Jack Reacher) (#2)_Lee Child

"I didn't ask you where she came from," Milosevic said. "Where did she head when she left?"

The woman paused.

"I didn't see," she said. "I took her garments through to the back. I heard the door open, but I couldn't see where she went. I was in back."

"You just grabbed her stuff?" Milosevic said. "Rushed through to the back before she was out of here?"

The woman faltered, like she was being accused of an impoliteness.

"Not rushed," she said. "Miss Johnson was walking slow. Bad leg, right? I felt I shouldn't stare at her. I felt she was embarrassed. I walked her clothes through to the back so she wouldn't feel I was watching her."

But it doesn't seem to have made it into the dictionary yet.

Yes, walking something could also mean “walking with” for example ‘I walked my dog’ That means bring it out for a walk.