The pressure wave is ultimately caused by displacement because of the volume of the aircraft, lift, and engines. We cannot really get rid of any of these. Given enough time, a strong enough pressure pulse will steepen into the double-shock 'N-wave' (because the pressure signal is N-shaped) the sonic boom.
Sonic boom mitigation then means to prevent the pressure waves from steepening into a boom before it hits the ground, e.g. by a long nose, lift distribution over a large part of the aircraft length, putting the engines on top so that their pressure wave radiates upwards, etc.
And if you have multiple, subsequent shocks (one at the aircraft tip, another at the engine inlet, another at the wing, etc), the later ones will eventually catch up to the first one, resulting in the N wave we would want to avoid.
So this new product will be limited to the same routes as concorde (plus pacific if they manage extra long haul).
Our knowledge of transonic aerodynamics and aircraft design have improved considerably sense then and much of the "common" knowledge that sonic booms will shatter windows and disrupt everyday life as a plane flies overhead at cruising altitude are very much outdated.
The problem with Concorde on approach/departure was largely a function of its engines, rather than speed. https://hansard.parliament.uk/Commons/1973-07-18/debates/427... shows it was comparable to slightly older aircraft at the time of introduction (VC10, B707, DC8) but notably louder than what was arguably its biggest competitor (747-200). In later years, continued improvements in aircraft noise pollution meant the margin between Concorde and other aircraft operating out of LHR just grew larger and larger.
It is probably part of their "secret sauce".
It was pretty cool because it was close enough to takeoff that you could easily make out the distinct shape of the plane.
I don't recall it being significantly louder than any other aircraft I've been near, but the vast majority of aircraft that were any where close were military aircraft!
>In the late 1950s when supersonic transport (SST) designs were being actively pursued, it was thought that although the boom would be very large, the problems could be avoided by flying higher. This assumption was proven false when the North American XB-70 Valkyrie started flying, and it was found that the boom was a problem even at 70,000 feet (21,000 m). It was during these tests that the N-wave was first characterized.