Traditional woodworking and blacksmithing like that is now mostly a novelty in the developed world. No one really knows how to make their own tools from scratch which is what it’d take to bootstrap carpentry. The best realistic set of skills would probably be knowledge of how to work with fibers to make rope and gather pitch for adhesive. Then you could make a primitive axe that can do most of the hard work in bringing down and hewing trees.
I’m not an especially good carpenter, and I can work with limited tools. A chainsaw and an auger drill would be really nice, especially if I had to make lumber.. but an axe , drawknife , and chisels will do.
That’s like being a programmer that can’t write software without a framework and libraries. The idea is that tools make the job easier and faster, not that you don’t even understand how to do the job, but only how to staple code together. We all start out there, and while we may rarely if ever work that way, we can when it is needed, do something no one has done for us.
Obviously, different trades have different utility if you are talking about the breakdown of society, but I’m not really leaning into that particularly hard, more leaning into the breakdown of one’s plans or expectations, the failure of a company or the evolution of an industry, those kinds of force majure events that one can reasonably expect to have happen during a life lived.
Even so, there is some comfort in knowing that your personal knowledge and value to society is robust and resistant to black swan events, I suppose.
Deserted islands don't have libraries.
Carpentry offers limited applicable skills if they're stranded 1000 miles away from the nearest Home Depot.