Old Codger Those slides can be a real PITA when they get stuck.
first thing I'd try would be to remove the whole kitchen from the fixed slide in the camper. In your 2nd photo there is a little plastic tab. To remove the draw, pull it out just so you can see that tab, hold that up or down (depends on which way the slide is mounted) and carefully pull the kitchen out to release it from the draw slide, it will only need to be pulled out around an inch or so to release it. You dont have to hold and release both slide's together, they can be released individually.
If it comes out you can then fix the problem and then slide the draw back into the runners.
Here's a photo of the slides on my camper. there is a little engraved arrow showing which way to hold the tab to release the slide.
If that fails you may need to remove the whole runner assembly and kitchen as one piece from the camper.
Bnk