The Bernoulli equation as a statement on the conservation of energy as I understand it is the observation in an idealized flow that the bulk fluid velocity relates to the kinetic energy of the fluid and must therefore increase/decrease to agree with the conservation of energy in the system. The internal energy of static pressure must be always "converted" into the kinetic energy of bulk fluid motion or vice versa. This is often used to explain why pressure gradients form to drive fluid flow.
I don't find that description of pressure gradient particularly satisfying because it is simply a relationship between the "types" of pressure in a fluid. That description only observes after the fact that when fluids have been accelerated there "must" be a pressure drop that formed due to a static pressure change since velocity changed. This does nothing to address the causality behind a pressure gradient even forming. The fluid seems to magically go from high to low pressure and accelerate because it needs to.
Obviously, to accelerate/decelerate a fluid, a pressure gradient must form to create an unbalanced force. Imagine the classical idealized example of a fluid flowing through a narrowing tube. It's velocity must have increased to agree with continuity/mass conservation. But according to Newton's 2nd law an unbalanced force must have changed the velocity. But the standard agreement is that the unbalanced force exists due to a pressure drop that the fluid moves through. But why does the pressure drop just automatically exist? How does the fluid actually know a pressure drop needs to be formed. Certainly, the higher velocity cannot exist in the narrowing first, before a gradient even formed. So how does the pressure start lowering in the first place, if at first the velocity and kinetic energy couldn't have increased without the existence of a pressure gradient? The causality of this makes no sense to me.