Yes you are right: the flag doesn't force star shinies. The same byte appears in standard event raids, as well as Dynamax crystal raids (tho it has yet to be used as this point)
For my example earlier, I was referring to event raids, tho I suspect a similar mechanism also exists for standard den raids (I need to check back on the shiny byte in pkNX).
Besides the fact that I've tested the byte for event raids, there's also wild area events that proves the point: recall the forced Shiny Magikarp, Shiny Clefable, Shiny Gourgeist, there were all forced square shiny.
It appears they don't have a byte to switch between Square and Star shiny.
The forced shinies results in squares. (as seen under shiny status)
Ultimately, without going into the argument of "which shiny is more special", because that is subjective (i.e. depends on the eye of the beholder), it is a fact that Dynamax Adventure shinies are locked to XOR=1. If you want square shinies, just import the mon from a previous gen. Pokemon from past/other games typically can be Square or Star, with the exception of Shinies from PGO; certain code in the game forces any shiny from PGO to appear Square, just like Fateful Encounters.