I believe, and we're at the edge of my understanding here, that the satellites need a consistent adjustment for local relativity. Because the satellites also have their clocks tick differently.
So they define a new time standard for the moon so that lunar operations can function based on that time standard, rather than having to recalculate relative to earth.

https://arxiv.org/abs/2402.11150

That's the paper from NIST that's basically the timezone part of it all.
They're basically defining how to calibrate moon clocks so we all agree exactly how they differ from earth clocks.