End game endless metal production
The Metalwood Tree
There is a real life process of producing lumber that is as strong as steel and completely fire resistant. It takes regular wood and through a process similar to making paper, produces this product.
For the purposes of Timberborn, maybe this can be a special researched tree that takes 60+ days to grow, and needs to be processed in a special building, perhaps a chemical steam press, before it can be used as metal.
The Hyperaccumulator Plant
Alternatively, there is a class of plants called "hyperaccumulators", in where the plant is able to extract specific metals from the ground.
These plants don't harvest large amounts of metal and take significantly longer to extract than what humans are capable of, but the purity of the metal is good, so having a farm sized plot of them should produce a decent amount of metal for beavers to use.