Yes there are a lot of stars. It's a big number. But there's a lot of space. That's a number that's in a whole different league.
For example, the whole solar system is about 2 light-day diameter. But it's 4 light years from the nearest star in any direction. Empty space is thus many orders of magnitude more than solar systems, never mind suns.
Sure there's a probability of a collision. But even multiplied by the number if stars, it's still really tiny.
Gravity tends to bring heavy objects together
Andromeda and the Milky Way are not colliding "like two pancakes on top of each other" but at an angle to each other
Also star surroundings are usually places where you can collide with a lot of stuff (asteroid belts, dust, etc)
We're not shooting a goal on a 4 light-year wide goalpost (btw that's the density on our vicinity, but on other areas the density is higher) but passing multiple stars on an environment that can be perturbed and heavy things attract each other
If they merge in 7 billion years, you think over the eg next 7 billion there won't be kinetic collisions? I'm skeptical.
Also watching stars getting disrupted by black holes would be similar.