Maybe I am being thick, and overlooking something.

Is there a way of adding objects/inventory items in the GB mode? Because I cannot find it.

The text at the create new game page where you choose between TA and GB hints that there might be - or is this just linking to another section of the book and, for the time being, all inventory items need to be recorded manually?

Gamebook mode was made very lately, it's not that advanced. So you need to stick without an inventory/record items manually.

However, you can use the normal TA mode, in which you can record items, to make a gamebook game. It's kind of simple. Make a few string lists with the choices as the strings, and in the start script, show the first list, after choosing the second/third/fourth list, then the fifth/sixth...
When the player enconters a choice where they pick up something, move the item to the player. Althrough this way is a little difficult and timetaking. I suggest you make inventory-less gamebook games.