Photos, as always...

I really need a apicture I have never seen a suspended ceiling in an outdoor kitchen.

The whole thing needs to be redesigned. There’s a lot of unsafe things happening in those pictures. An indoor range— outdoors for the wiring to corrode and be a fire hazard. A range in front of a window. A range with no hood, depositing grease on an exposed wood flammable surround.

Guy it and start over completely with with a good Kitchen Desiger.

We know it's rough which is why we're working on it. For example, we are getting rid of the range because it's such a hazard (pilot light outdoors in a windy area, no just no). But, we still need ideas for ceiling product.

Assuming you're getting rid of the stove (and abandoning the idea of cooking in that space,) you might try a V-groove wood plank that looks like what's under the deck.

Now that I see it, I think vinyl may not be good because even if you just use a hot plate out there, there will be heat rising up that could soften it and make it warp. It seems like a place you might want to use an electric smoker or other appliances like that, so you want to handle heat well.

What about a metal ceiling tile, in a color that works with your space? I know the square ones can seem "too victorian" in some applications, but when painted a deep color in a matte finish they look less feminine. Or, if you want to channel a modern/industrial vibe ... corrugated tin can be a cool ceiling.

Corrugated tin is not a finish material unless you're building a Quonset hut. Or maybe a carport in West Virginia.

When you posted about a suspended ceiling outside, I did not expect a typical suspended ceiling like that. That's...unique.

There's no reason not to put a proper ceiling there--certainly something like v-groove as scottie mom suggested. I would not do drywall, obviously, but something sturdy. Check Hardie and see if they have any cement board products that would work.

We've done it a couple ways. Least expensive would be pine tongue and groove ceiling. Inside porches/under roof cover they're not really exposed to the elements in the same way as the flooring. We've used AZEK (pvc composite) sheets for the ceiling, using AZEK 1'4s to cover the joints and give a decorative grid pattern. And then, AZEK also makes a tongue and groove product. Depends on budget and what the finished look will be

I would remove the walls finish the ceiling like under your deck and make a proper outdoor kitchen