As seen here on the info box for Stalin, giving his name in Georgian/
Doesn’t look like it’s derived from Cyrillic or Arabic; is it from a Persian alphabet?
Following the links to the page on the Georgian alphabet, it appears to have been an independently created alphabet though the order of letters were influenced by Greek.
Although it appears to be a subject of debate among the sources of that wiki page.
It might have been invented by an Armenian guy who also created his language’s alphabet. Armenian is more obviously Greek/Latin in appearance.
The fact that it was a created as a new alphabet does not seem so much in debate as much as the question of who invented it. There do no appear to be any non-Georgian antecedents.