The question appears to be answered in the ruling, which @EddyTeddyFreddy kindly linked to in this thread:
Based on a quick read-through, it looks like Trump jumped the gun on Judge McBurney and filed his “appeal” before there was a ruling by Judge McBurney.
The Petition for Writ of Mandamus was denied because the Georgia Supreme Court believed it was premature and not properly before them. Moreover, they pointed out that even if the Petition had been properly filed, Trump’s remedies still would not include a basis to quash the proceedings.
Boom! (As they say.)