The OP is asking about how it from the power company point of view. In addition to power and VARS, each kind of load has different transient characteristics. The OP mentioned harmonic injection.
For example, some utility engineers are concerned that LED, incandescent or fluorescent lighting each has different load characteristics. Motor loads have inrush currents during startup. Utility engineers model those differences in their grid simulations.
I doubt if the chips in a computer make a difference to the power grid. The power supply (PSU) is the load seen by the grid. IMO no DC components downstream of the PSU are likely to be significant.
When I said I didn't know of special purpose hardware for bitcoin mining, I was thinking about non-digital-computer hardware that might connect directly to the AC mains. I'm pretty sure no such exotic stuff exists, but I'm surprised every other day by something new.