This conflict is a real shitshow... I have no idea how it can be ever resolved, besides just waiting multiple generations until various ethnic groups move (or mix...).
The official map shows an Armenian exclave in the middle of Azerbaijan, and the reality is even more difficult. In the past, Soviet leadership tried to change the demographics by importing Azeris into the region︀ which didn't work as planned. Now Armenia borders Azerbaijan and also Turkey which declared it︁ can support Azeris with an army. Azerbaijan borders Armenia and also Russia which on the︂ other hand would probably support Armenia.
Georgia borders both countries but probably cannot side with︃ either one, culturally and religiously it is closed to Armenia but economically it is closer︄ to Azerbaijban and it doesn't want to lose the business and tourism coming from both︅ countries...
Oh, did I forget both countries also border Iran and the Kurds? Many Iranians︆ bank there because they would be rejected absolutely everywhere else.
Even given all this, I︇ still wouldn't expect your money in an Armenian bank to disappear or be confiscated. The︈ risk will be something more subtle will happen - a) inflation of the local currency︉ and b) restrictions of handling with euros and dollars. If you need inspiration of what︊ can happen when a country gets into a political and monetary crisis, look at current︋ situation in Lebanese banks.