What sort of wooden vehicles can you make/use?
Carts and boats.
2 tile carts are pretty manageable.
I’ve made a folding wooden mini-motorcycle. I use it to drive over to distant cars (my current base in a Mansion) and then fold up the bike and drive them back to base to be disassembled for parts.
You could literally make an entire semi truck trailer if you didnt mind it being slower than a sloth with all the carrying capacity of a sloth
I remember once a long time ago I made what was basically a motorised wheelbarrow for my tree felling needs. It had two wheels, large electric engine, seat, trunk, solarpanel, controls, large storage battery, and I think a floodlight.
You can really create whatever vehicle you want
It’s very handy if you can’t find a trolley but need some sort of wheelbarrow type contraption to cart your loot around in. E.g. if you’re trapped in a lab start or something. Given how widely available broken down cars are to cannibalise though, I can’t see a lot of reasons to use wooden vehicles outside that. I suspect it doesn’t even have a weight advantage compared to e.g. bicycle parts.