Armenia is a Russian vassal state. They fell into this position out of necessity. Russia will not intervene in Artsakh/Nagorno-Karabakh, but will defend Armenia proper. A red line would be crossed, if Azerbaidzan/Turkey tried to cut Armenia's corridor to Iranian border. AFAIK this is currently the only route Armenia can get weapons & ammo. This escalation is unlikely to happen. With or without Turkish support, Azeris would be unable to defend themselves against Russia.
Georgia is officially neutral, but allows Azeri Silk Way Airways to fly cargo (i.e. weapons & ammo) from Israel and Turkey through its airspace. So they have already chosen their side, partly out of economic necessities.
As to Armenian banking, the biggest risk is the coming economic hard times. A costly war + partly self-inficted corona damage may cause all kinds of troubles, such as dollar shortage.