I've only an A-Level in Further Maths from 1997, but understand complex numbers and have come across complex inverse trig functions before.

My takeaway for other people like me from this is "computer is correct" because the proof shows that we can't define arccosh using a single proof across the entire complex plane (specifically imaginary, including infinity).

The representation of this means we have both complex functions that are defined as having coverage of infinity, and arccosh, that a proof exists in only one direction at a time during evaluation.

This distinction is a quirk in mathematics but means that the equation won't be simplified because although it looks like it can, the underlying proof is "one sided" (-ve or +ve) which means the variables are fundamentally not the same at evaluation time unless 2 approaches to the range definition are combined.

The QED is that this distinction won't be shown in the result's representation, leading to the confusion that it should have been simplified.