You can eliminate the ‘on the desk…’ message by saying
The examine supporters rule does nothing when the noun is the desk.
The examine supporters rule lists anything that might be on a supporter when you examine it. The thing you need to do is make sure you have some other way for the player to see what’s on the supporter, such as placing a list of those items in brackets within the description–
The description of the desk is "You like to put a lot of things on this desk, which now has [the list of things which are on the desk] on it, as it's the only surface in the room."
To prevent the ‘you can also see’ message, you can also give the object an ‘initial description’ paragraph–
A painting is here. "Hanging on the wall is the notorious painting". The description is "[if the player is John]You hate this painting, but Mary loves it[otherwise]You love this painting, but John hates it[end if]."
Initial descriptions are put in quotes just like a room description, without a ‘the description is’ (which would make the sentence the description of the object when examining it). When the item is picked up, however, the initial description is no longer displayed when the object has been dropped (after which you will get the ‘you can also see’ message).
But as you stated, you want it only in the room description. You’re getting that message because the room description is printing only the ‘unvisited’ message–so the painting is still ‘unmentioned’ when the parser gets to the ‘you-can-also-see’ stage, where it prints the list of take-able objects in the room. It won’t get to the [painting], because your [if] tokens skip over it in the initial turn, so the painting goes ‘unmentioned’ and gets mentioned at the you-can-also-see stage. So what you can do here is say
Before listing nondescript items in The Office:
if the painting is marked for listing:
now the painting is not marked for listing.
That will discount the painting from the list of nonscenery items in the room, which are not on or in something. The thing about this is that you will want to change your room description to reflect the painting (and other objects like this) having been taken or moved.
You don’t have to say ‘A painting is in the Office.’ You can make it ‘A painting is here.’, as long as the Office is the most previously mentioned room as a subject of a sentence (such as ‘Office is a room’ or ‘Office is south of Tipperary.’).
I hope that this helps!