Read an article on gamerant - they gave a tip that if you can't see the chair in the options, you have to claim the reward, which is the chair.
Having the same exact issue as this^^
I was having this same issue. I had the reclaimed wood dining chair reward claimed. I was finally able to complete the quest just a few minutes ago. I don't know if it will work for everyone but I had to start a new save, disable the mods. Put the Reclaimed Woodwork Table in my sims house and had her build up the Handiness skill on the table. Once she reached level 3, I clicked on the table again and she was able to craft both chairs. I hope this helps others. It's a few suggestions I saw others try and figured I give it a try myself, because I was having this same problem for days now and just able to complete the quest this afternoon.
