The engine that does this (except using a fixed inlet instead of a multi-chock inlet) is the GE Affinity. It flies between M0 and 1.4. The problem for the Boom project is its leaders who didn't know better put the bar at 10% faster than the Concorde, that had the luxury of a straight jet (and the consequential take-off noise). You can't handle the Ram drag at M2 unless you can limit the amount of air mass that enters the engine. It's physics, every engine designer knows about it. This is why the Tu-144 changed from a bypass engine to a straight jet during its development.https://paxex.aero/2020/07/boom-supersonic-rolls-royce-engine-partnership/
It is not a new technology engine, it is a new design engine. You’ve got knobs on an engine like bypass ratio and pressure ratio and they’re set in certain places for the 787 and you want to set them in different places for this airplane. It is moving the knobs, it is not let’s invent variable cycle or something that’s never been certified before.
Now, it's possible as the article says, that this will turn out to be impossible. But for right now, Boom definitely seems the possibility of something a lot less demanding that a new core and a variable cycle engine. A lot can be done with inlet and nacelle design, especially since they are really only trying to optimize for a single point performance, unlike the multiple points where military engines are trying to work. Having lots of excess thrust so they can take off at partial power seems like a simpler, if less efficient, solution.