Well, I can say you’re not alone, as my 2012 Pursuit will sometimes leave its cluster lit up line your first pic when I shut the engine off. It’s not very often, maybe a couple times a month, but I have not been able to find the cause so far.
I have figured out that when I catch it doing this, I can simply cycle the ignition through ACC, RUN, and then back to OFF, and that will leave it in its normal state (cluster lights go out after appropriate amount of time once door is shut). Unfortunately it sounds like this workaround doesnt work for yours. The next best thing I can think of would be to dim the cluster as much as possible with the dial by the headlight switch. That should reduce its power draw enough to keep it from draining the battery by morning.
On the subject of this draining the battery, I will also say that this shouldn’t be enough on its own to drain the battery below the level needed to start it (after sitting overnight). The fact that yours is getting drained tells me something else is drawing power (probably related to this issue), or the battery is badly sulfated.
How old is the battery?
Check the physical appearance of the battery for signs of sulfation. The sides of the battery case will bulge outward when it’s in such a condition, usually enough to be visibly detectable. Take it out and go have it tested at a local auto parts store if there is any doubt.
Also, what is that 2nd picture showing? I see what screen, but why did you include it? It’s a different state than the first one. We’re you able to get to that screen with the ignition OFF?
If so, that’s going to be the problem - the ignition is not going into the OFF state. Figuring out why will be the focus from there I would think…
