I went to the woodworking table as a level 10 in handiness skill and there is no option for the wooden throne. So I made the toilet hoping that would complete the mission, I know it’s not the same but I tried it. Of course it didn’t work.
Also, I went to the cave and in my game it’s already broken into, so I explored it and it didn’t check off the mission from the list.
I have this same issue. I did everything except the final task, which is to build the wooden throne. Level 10 handiness, but the throne does not show up in the pie menu. Still hoping to find the solution to that issue.
On the other hand, I was confused about the cave, too, since I'd already broken into it. But then a message popped up to "share" thoughts or experience (can't remember) about the cave with two Sims. Did that and it worked.
Hopefully I can figure out the throne issue, since that's all that's left for me.
EDIT TO ADD: I found the solution. Claim all available "rewards," the last one being the wooden throne. Once you do that, the wooden throne is available in the pie menu for the workbench. YAY!
