I would not expect there to be a problem with the squashed cable, but clearly one can't be sure, and really no way to test without damaging the cable. But an insulation resistance test would satisfy me. As long as correct fuse/MCB fitted and RCD protected I can't see much of a problem.
As to tumble drier on an extension, for a resistive heater type, they use a lot of power, often over 2 kW for an extended time, and there is a question as to if should be on a dedicated supply anyway, although often they are not, the only item in the house below 3 kW which is likely to over heat a supply more is the immersion heater, but we all including myself tend to cross our fingers and trust to the Lord, and worse case scenario seems to be blown fuse or tripped overload.
However with a heat pump type the scenario is very different. It uses less power, and also cycles on/off, so unlikely to ever cause a fuse to blow or a overload to trip, except for any overload built into the unit. The problem with any refrigeration plant running on single phase is the time it takes to start, and the time it takes to build up pressure, the motor needs to reach run speed before the pressure increases to a point where it can stall the motor, a internal overload is included and if this trips on the odd time, when for example the unit is unplugged then plugged back in before the pressure has dropped, then the internal overload will do its job and turn the unit off, then back on latter when it has cooled and the pressure has also dropped. However if this happens repeatedly then the overloads often burn out.
So volt drop on refrigeration units is important, near every freezer states do not use extension leads as a result, it seems to be a standard entry in the users manual, even with inverter models which have three phase motors so really no problem, or at least not until the volt drop is huge. The inverter reduces the inrush and compensates for volt drop, so not really a problem, the one item I found the problem with was AC units used in porta cabins, which used more power than a domestic fridge.
I have no idea what is inside the heat pump tumble drier, it may have an inverter, but I simply don't know, I know it dries my cloths, and uses less electric, and I would use as short as an extension as I could and as heavy of an extension as I could, and nothing else on same extension, since the motor switches on/off so often I don't think I would know if it tripped the built in overload, to be frank I have never sat and watched it. I switch it on, and return when I hear no noise. Most items out of interest I have used an energy monitor with, but never bothered with the tumble drier.