Agreed. I modeled it that way because it looked like that from the original but it’s a quick fix.
As you can see I made that change. I added a shallow dado in the shelf to help locate the upper side panel and make a cleaner join.
Welcome to the club. Good excuse to buy more tools, too.
Good deal on the new computer. Make sure you install SketchUp correctly when you get it. That means right clicking on the downloaded installer and choosing Run as administraor from the Context menu.
One thing you’ll want to get a handle on is correctly using groups, components, and tags which used to be called layers. Remember that tags don’t provide separation between geometry. You do that by using components and groups. Tags are only used to control the visibility of objects (groups and components) in the model. ALL edges and faces should be created as Untagged and remain Untagged.
As you may have found out, when you edit one instance of a component, all other instances get the same edit. That is extremely powerful. For example when I made the change to bring the shelf all the way across and add the miter to the right end and the dado for the upper right side, I only had to make those changes in the assembled version of the model and I knew the changes would show in the exploded view too.
If you want to make an instance different, though, you can right click on the component and choose Make Unique from the Context menu. For the case I only drew the left side, bottom, and back. The other verticals were copies of the left side. The horizontals were copies of the bottom. In each case I used Make Unique so I could edit them and make the needed changes.