I’ve made large things in my laser-cutter in the past. Look up some of my projects on this forum, and you’ll see some large items.
These thread in particular talks about an arcade cabinet I made.
It’s all about using thinner material and gluing up layers to make larger items. I’m not sure how sturdy a chair would be. My arcade cabinet, and the art pieces I make feel pretty sturdy, but they are not structural. I’ve never tried to sit on them.
Essentially, you want to take the part you want to make, and break it up into pieces that fit on the GF bed. You then do that again, but break it up at different places. Try and keep the break points as far from the first break points as possible. Then you glue those 2 layers together. Then you do it again for a 3rd and/or 4th layer. If your break points are at different places, it should be pretty sturdy.
For the arcade, I also cut registration holes. So that I could line up all the parts while I’m gluing them. Typically, I use 1/4" registration holes, and slide 1/4" dowels through the parts to line them up.
I’ve never tried to do a living hinge in this fashion (like the one on the Alex Chair you linked). But I imagine it’s possible.
The fact that it’s 1/2" birch plywood means you have four 1/8" layers to work with. You can put your seems in many different places.
It would be an interesting project.
Let me know if you need me to clarify any of the steps I take. I love making big projects from small parts!