Earlier quoted context omitted.
Yeah but you are getting 50:1 difference in energy density between hydrocarbon fuel and battery. Also, vertical takeoff is extremely inefficient because a wing can generate a lot of lift compared to drag. this in addition to the fact that a vertical lift system is only used during take off and landing while being dead weight the rest of the trip. even elon can't override physics
The big power requirement of VTOL is not the problem in the overall energy budget because the hovering time is very short compared to the total flight time. Main problem is the additional weight of the more powerful engines. BUT: If you want to fly supersonic, you need very powerful engines anyways, so if you can re-use them for VTOL it's a win win.
VTOL requires an engine that is powerful at low speed.
The harrier jump jet, a most famous VTOL aircraft, didn't have supersonic capability when all its contemporaries did and can only take off vertically with reduced payload or it would burn all its fuel just taking off.
While I don't have the numbers I think VTOL supersonic aircraft would be VERY hard indeed and it would be something that has to be seen to be believed.