I’ll just address the two parts together. Bernoulli’s equation is about how pressure and velocity change as a bit of fluid moves along a flow line. It comes from the conservation of the energy of that bit of fluid.
So let’s follow it along. In the combustion zone, the gas is hot and under high pressure, but not moving very fast. Next it goes through the nozzle, where the gas speeds up and the pressure drops. This initially reaches its limit when the pressure has dropped to atmospheric pressure right at the end of the nozzle. At that point the gas is moving as fast as it can, and as much of the combustion pressure as possible has been converted to velocity. (You want that to get maximum thrust)
In space, you can take that further, dropping the exhaust to even lower pressure and getting more speed. More speed is more thrust. This is an advantage of having a “vacuum” engine on a rockets upper stage.
Another way to think of it, not using Bernoulli’s equation but just as valid, is to think about the gas in the middle of the nozzle. It has high pressure pushing hard from the combustion chamber side, and much less pressure pushing from the atmosphere/vacuum side. What will it do? It’ll accelerate away from the combustion chamber toward the outside, gaining speed as it does.