The analog algorithm described is not described for digital computer. It’s an amusing theoretical thought experiment and not a recipe for actual fast sorting. It’s O(n) when you use your hand for contact and removal. I don’t know if it’s possible to implement spaghetti sort on a computer, maybe not, but I guess if it were possible, it would probably at least require n processors to sort n elements. Maybe the nearest analogy on digital computers is radix sort.

Depends on the mathematical framework you're working with.... there's a genre in theoretical compsci that deals with parallel algorithms, and as a toy example, I remember an O(1) sorting algo (given O(n^2) processors). This example is more fun than anything, but ofc in general you're free what constraints you subject your statements to.

You can simplify the "human hand" to a rigid metal sheet that comes down from the top and stops on the highest object. Still constant time, but no "parallel processing" needed.

The point is that reality itself is highly parallel

You're talking about some other kind of sort.