Baku seems like an odd choice, given the visa requirements for EU citizens which could cause issue if the plane had to be taken out of service for any reason. Tbilisi looks to be on the flightpath and Lufthansa do operate there, which is visa free for EU passport holders.
The original flight with Privatair went via Bucharest on one leg only. The A319 has shorter legs so needs a stop both ways for a drink.
For EU travellers this would have been no problem. Though as a non-Schengen country it would still have been a problem for Indians.
I would assume that should there be a problem in the future they would do as they do if a plane has to ditch anywhere unexpectedly; sort something out on the ground. E.g. when the Air France plane had uncontrolled engine failure, or that BA 787 recently ditched in Iqualit, or whenever something has to divert into deepest Siberia.
Though I agree they perhaps could have arranged for something like Turkey with VOA for the majority of Europeans. For Indians they still require a visa, though it's granted online if they have a Schengen stamp (which they would coming from Germany). The only hitch is they are required to travel with either Turkish Airlines or Egyptair (seems draconian).