Thank you for the much needed correction.The offense does not need to be a felony.
In addition to the written law (which as you pointed out, is expansive in what powers it gives citizens "any offense"), the Georgia Supreme Court has made several rulings regarding citizens arrest.
These include at least two cases where the Georgia Supreme Court found that the amount of force used was not warranted by the totality circumstances (shooting a shoplifter, using baseball bat on a fleeing burglar).
What Is Georgia's Citizens Arrest Law — And Why Are There Calls To Repeal It?
In the end, the written law in regards to citizens arrests seems to have been supplemented by case law.