Another idea is to make a turbo-jet engine heated by electricity instead of fuel.
If we consider the reason one wants to travel at supersonic speeds, we might arrive at something involving the value of a human's time. Given that, slow but ultra efficient, luxurious (and internet-connected - "workable") travel might be something. Then gliding, floating, etc. with ample space and creature comforts could be the focus.
I was going to decry the inefficiency, then remembered that a resistor is only device with 100% efficiency.
You could collect a lot of heat from the airflow over the body. Meaning there would be a lot of air with some level of heat that’s constantly being replaced.
And if it were, wouldn't it be just more efficient to glide at lower speeds?