I would say that any activity that adds value to an existing object generates wealth. If you take a tree, cut it down, debark it, saw it into timber, and kiln-dry it, it is worth more than it was as a tree. Or at least it’s more utile.
Similarly, if you take a shipment of sheet metal and stamp it into fenders that you then paint and buff, it is worth more than it was as sheet steel.
That is Karl Marx’s Labor Theory of Capital. Which he despised, by the way.
Yes, any activity such as you mention of cutting down a tree and processing it into more useful items does create a minuscule amount of health. You can say it is a form of manufacturing.
However in the overall scheme of things, the real giant wealth creators are manufacturing in factories and mining for chemicals, oil & metals. Perhaps 85-90% of wealth creation.
Where was the tree grown?