Maximum object number: 254
Maximum number of objects: 254

Once you try to create a new object at this point, the Item Editor replies, "There are no empty slots left."

The following object numbers are reserved:
0 - Nothing
1 - Money
255 - Creatures

I checked the U4PART2 game, and it uses 252 objects, numbered 1 to 254. There are two gaps. So I think that may be a good guideline. You could also create a dummy game, and keep creating objects until you get an error message, and find out the maximum that way.

The exported OBJECTS.TXT file does have a complete list at the end, in numeric order. It doesn't say which numbers are unused. Perhaps if you import this list into a spreadsheet, you may be able to count the rows - or match up object numbers to row numbers.

I exported objects txt to find out how many I have left to make. It did not tell me this though. I was hoping as when you export regions, it will tell you have many types of stuff you can still add to the map. But the objects report only tells you what has been made already.
Of course their can be only 255 or 256.
During the course of making the game, I found a better way to make some stuff so I deleted objects I no longer needed.
When we delete objects, the order of the objects doesn't change. Instead you now have unassigned numbers in the stack. And when we make new objects after deleting old objects, they new ones take the number of the old ones.
This is a problem for me because not sure how many I can still make.
I am up to 244 or something. I would like to leave the last for items I know, or find out I need to make later. Since I have deleted some objects before, It's not up to 244. Instead I keep making objects with lower numbers.
Is there a way to find out? Or do I just have to keep making them until I run out?