>> The mega-constellation sweet spot ... multiple planes in a single launch.
Mega-constellations are exactly the type of project that doesn't need multiple planes. They require multiple sat in each plane, meaning one rocket full of small sats can go to one plane and dump them all. I suspect something has been lost in translation. I think they mean to say that the relightable engines will allow access to different altitudes on a single launch, multiple orbits within a single plane.
Inclination changes are expensive, so if you want different inclinations, it almost always makes sense to use a separate launch vehicle for each inclination you want to target.
However, the longitude of the ascending node (Ω) is perturbed by the earth's oblateness, and the rate of Ω precession is a function of the semi-latus rectum (p) and the inclination (i). If you adjust the orbit altitude to tweak p, you can adjust the precession rate to swing the plane around to where you want it.
This takes a while (months), and you of course need some sort of propulsion on the spacecraft to return you to your target altitude after the maneuver, but if the launch vehicle can drop you into the higher/lower altitude above/below the target plane rather than doing that on-board the spacecraft, the delta-v cost is halved.
I would call that on-orbit maneuvers rather than part of the launch process. This rocket will drop the sat off at the contracted orbit and fly away. Multiple engine firings will mean separate customers can get at best separate altitudes.
Mega-constellations are exactly the type of project that doesn't need multiple planes. They require multiple sat in each plane, meaning one rocket full of small sats can go to one plane and dump them all. I suspect something has been lost in translation. I think they mean to say that the relightable engines will allow access to different altitudes on a single launch, multiple orbits within a single plane.