Passenger transportation between the occupied territories of Ukraine and Georgia is carried out by several transport companies. One of them is Sputnik. Site s-putnik.info The fare is about 300 USD per person, there are discounts for children. On the way from 1.5 days or more. The first bus takes you from your city to the border with the Crimea, after a walk you change to the next bus to Vladikavkaz, and from there on the third bus through the Upper Lars Pass to Tbilisi. Then you can stay in the capital, fly to Europe or move to any other city in Georgia.
Also, there are private carriers in their cars who take fellow travelers. Contacts can be found in the relevant thematic publics and chats in Telegram, Viber, Facebook, etc.