I have had cousins of my family from mixed Azeri-Armenian families have to hide inside my grandparents' home in Baki during the 1990 pogrom. I have had male relatives also be unable to leave their homes for a few years because of fear of being kidnapped on the streets and being sent to the front lines. I know that for some this is an irrelevant, almost funny spectator sport-war, but war really isn't what most want or desire. With a lot of the borders being drawn by imperialist chauvinist Russians during the empire and soviet period, both groups of people are victims of imperialist violence and the consequences of empire. Azerbaijan, especially, being an all-but-dictatorship, really doesn't reflect the desires of most people (including my grandparents); it's a government that cares very little for its people and it's no surprise it'd take such terrible actions. The losses and scars of the 1990s are still felt and remembered, and of course part of that is manifested as animosity.
Of course, framing this poll like you did only plays into the hands of Russian, Turkish, and dictatorial desires - the people of this region are mere toys for their exertion of power. And of course BRTD effectively rebranding this as a crusade against the invading Islamic Azerbaijani horde is disgusting, let alone inaccurate considering how secular the country is. But it's a stupid poll, reflecting its origin.
First I'm very sorry for what your family has gone through. I hope they are all safe now.
But it's hard to deny the reality here that Azerbaijan started this with missles and air strikes against peaceful Armenian settlements in Nagorno-Karabakh forcing most of the population into bomb shelters. It's an unprovoked act of aggression by the Azerbaijan military against an oppressed ethnic minority in the country.