The number of errors there is frightening. I only noticed the use of void-pointer arithmetic and lack of alignment processing.
I would say the code doesn't go far enough. Instead of using `std::unique_ptr<char[]>`, it should define some kind of memory_block abstraction (using `unique_ptr` internally), where the copy constructor and `operator=` both do a byte-wise copy of the data. Then alongside `make_contiguous`, you would have an analogous `copy_contiguous`, where the base case of `make_contiguous_helper` would instead call `memory_block.resize(total_size)` and the base case of `copy_contiguous_helper` would call memory_block = other_memory_block. This would remove the boiler-plate code for the copy constructor in Mesh, which can instead be:
Mesh::Mesh(const Mesh& other)
: memory_block(copy_contiguous(other.memory_block,
positions, other.positions,
indices, other.indices,
vertices, other.vertices))
{
}