There's also a sneaky path: the internal floating node voltage goes up and down, not quite in phase with the drain proper; the effect is, there's a burst of hysteresis loss when going through low Vds, where the top transistor is saturated and the bottom one is still pulling down (or letting go). This has a similar effect to SuperJunction hysteresis losses; it's a bit lower magnitude in typical cascodes, but nowhere near the level in planar devices (ancient Si*, current SiC, most HV GaN).
*Planar Si have low
output losses, but you make up for it in the several watts gate drive required to run a big enough device, fast enough to matter. Not to mention the cost of said device. So, uh yeah, this wasn't ever really relevant prior to SJ, not to mention the widespread adoption of resonant topologies.
GaN also have the concern that the channel to substrate loop can absorb some induced field, and this dominates the hysteresis losses. That is, the substrate isn't usually connected (or strongly connected) to the transistor, there's a buffer layer between GaN-stuff and the Si wafer. Either way, there's capacitance from channel to substrate, then resistance through it.
Mind, these loss effects are far smaller than those due to hard switching, or poorly timed switching in general -- it's mainly only noticeable in resonant designs. And GaN losses are noticeable in the several to 10s MHz range, so you'll be running quite fast to have that as a dominant problem.
That said; if you want to explore resonant, you could probably hack the '3842 to run QR flyback. Not sure there's any example circuits out there, and, there are proper QR mode controllers that could replace it, but, some clever manipulation of the RtCt pin / network, in relation to the aux winding's AC voltage, could be relevant here.
Tim