When stood up your heart has to pump blood over a larger height difference so will have to work harder.
Well, yes. The mechanism is to do with a reduced venous return when you stand – less blood coming back to the (right) heart, lower stroke volume, so lower blood pressure, then a compensatory tachycardia as you mention. So it is a normal response, and for most, indicative of healthy, elastic blood vessels – although not usually to the extent that tpbiker is describing. It will also be more pronounced if you’re dehydrated, so that may be factor.
There is a condition called PoTS where this response is exaggerated. It would be very unusual in the MAM(IL) population we have on here but feel free to have a read! https://www.heartrhythmalliance.org/stars/uk/postural-tachycardia-syndrome-pots