Irrespective of they are independent, Republican, or Separatist, how many systems are there in the Star Wars galaxy during the Clone Wars?
3.2 billion habitable star systems
According to Wookieepedia:
Factoring in the output of heat and light needed for an advanced civilization to form, there were 7.1 billion truly habitable stars within the Galaxy, and about 3.2 billion habitable star systems. However, it was estimated that about one billion of those systems were actually populated.