Is it possible to have an Ikea METOD wall cabinet with a drawer?

then basically a depth-reduced base cabinet

That’s why I spoke of the "principle" and just wanted to give you the hint that you can basically take the configuration from the base cabinets and simply swap out the carcass. Although I wouldn’t use the surface of the wall cabinets without a cover panel either. Unless you want to continue building upwards with the wall cabinets. There is also the 80x27x200 cm carcass for that.

Which surface do you have? Is it the Veddinge?

Yes. I had to check briefly. That is Veddinge. My wife wanted fronts from another provider (for now, ahem, 5 years), but she can't decide on a color. Back then we took the cheapest front, which could well stay that way.

just simply exchange.

Well, drill holes do matter at Ikea too. What looks doable is often tricky.
I first wanted to take Knoxhult without a drawer, but there are no drill holes at all, only one shelf is possible.

without cover panel

There should be four in a row. Who knows when I'll get around to getting a 240 cm countertop that isn't too expensive. So I’m using Plan B with the wall cabinets, since the TV will be standing on it.

My wife has wanted fronts from another supplier (for now *cough cough* 5 years), but she can't decide on a color.

We have the Stensund front in light green from IKEA and are very satisfied with it... It's relatively new - maybe it's something for you too.

Do you want to just hang them on the wall or also support them with feet? Because the pre-drilled holes for feet are only in the base cabinets ... naturally, since the wall cabinets usually hang with their underside in the visible area.

Because the pre-drilled holes for feet are only in the base cabinets

Yes, I know. We weighed it yesterday: rubber feet will be put underneath.