You don't make a complete copy: you make a shallow copy of the spine, and then only descend along the fields you actually modify. The number of operations scales as O(branching factor * depth), not O(size).
Sounds painful.
It works out cause I only use state of this complexity in a single spot. The code to do the copying does not read well in my opinion, and it definitely could get nasty in some cases (slower systems with updates on each keystroke say).
A library like Immer seems very reasonable if you are working on big nested structures often. Worth considering depending on the case.