Apparently, a major problem was that one of the two main thrusters failed, as its bell section departed the spacecraft, as Questioner noted. The root cause may be associated with an excess of oxidizer supplied to that thruster. He compared it to a similar problem, a faulty valve in Akatsuki, a Japanese probe to Venus.
_______________
Speaking of applicable expressions, we could say “thrusters up,” similar to “Tango Uniform,” derived from “belly up,” which is what happens to dead fish. Maybe we don’t want to compare a fairly successful lunar probe to a dead fish.

Or, “flamey end up, point end down” could be appropriate, although there aren’t any flames, anymore, and the pointy end isn’t really pointy.

Upside-down does not really fit, because as Questioner pointed out, the solar arrays were supposed to be on top, after landed, so it is really upside-sideways.
__________________
Getting space right is not easy. We have a lot of trouble with newly designed launch vehicles, despite them being similar to well established rockets (Starship and Super Heavy are trying to do very new things, which makes them even more difficult to get right). We have a trouble landing on the Moon, despite the many successful landings over a half century ago. Probes to Mars still go awry. When I was building and testing satellites and satellite instruments, the darnedest things went wrong, although we were able to fix the problems we knew about before launch. The concepts of rocket science may be simple, but executing them successfully is still difficult. We seem to still be in a steep learning curve, where space is concerned.

Then again, getting aviation right took a century, and yet we’re still learning.

How wonderful. My recollection is that is how the ship landed on the Moon in the book Rocket Ship Galileo, my second science fiction book, right after I Robot.

It was nominally planned that the SLIM lander, shortly before touchdown, would turn or tilt 90° from the starting position with engines downwards, so that it would come to rest on one of its side surfaces, on which a kind of small legs are attached.

Due to the engine failure (the expansion nozzle of one of the two 400N engines blowed off), this planned movement was now not just 90° but 180°. In the spirit of the device’s designers, the lander is not upside down, but on its side.

If it survived landing on its roof, how much does it need those crushable legs?

I had assumed that it touched down, then rolled over from too steep of an angle on the landing site.

My reading of the article is that it set down in correct orientation but due to its eastward speed it tipped over after soft touchdown.

From the press release:

… but conditions such as the lateral velocity and attitude were outside the design range, and this is thought to have resulted in a different attitude than planned.

Blair Ivey,
I’m still laughing.

I’d say the first was when JFK exhorted us to ” . . . set sail on these new seas.”

‘Up in the air’ may not be technically accurate, but does provide an immediate, understandable, grasp of the situation. It’s good communication.

I wonder how many anachronistic expressions will make their way into our space-traveling future. There are plenty of them still around on Earth: Hair of the dog [that bit you], hang up the phone, squeaky wheel gets the grease (I’m old and I’ve never greased a wheel; hurrah for sealed bearings), never look a gift horse in the mouth, fall off the wagon, etc…