Why high air speed at flat surface don't always produce low pressure?
TL;DR
Speed does not produce low pressure, increasing it does!
Bernoulli's equation says that for a fluid flow, in absence of elements doing work on the stream or having work done on them by the stream¹, $p + \frac12\rho v^2$ stays constant². But it does not tell us what constant. You can have flows with any combination of $p$ and $v$, and all will still satisfy the Bernoulli's equation.
Straight box in the first video
The blowers increase the energy of the air inside the hose. The energy can manifest as either static pressure, $p$, or dynamic pressure, $\frac12\rho v^2$. How it chooses? Well, if the static pressure $p$ inside the hose is higher than outside, the pressure gradient accelerates the air out, converting the static pressure to dynamic, and if the static pressure in the hose is lower, the gradient decelerates the air. So the flow will quickly stabilize so that the static pressure matches the ambient³, and the added energy determines the velocity.
Therefore there is the same static pressure everywhere and the box between the two nozzles has no reason to move.
Curved surfaces in the first video
The other experiments in the first video are not explainable by Bernoulli's equation alone, but instead effects of inertia and viscosity have to be taken into account. As the air flows around the curvature:

If the curvature is towards the stream, the air starts hitting the wall and needs to turn around it. Since it has mass, it requires force to turn it, which creates additional pressure on the wall, and a pressure gradient forms near it turning the air molecules further away. Bernoulli's principle tells us the velocity will, somewhat counter-intuitively⁴, decrease, but that is just a side-effect; we already know the pressure is increased.

It the curvature is away from the stream, the air would want to just continue straight. However there can't remain a wedge of a stagnant air behind the receding surface, because it would have higher pressure that forces it to move, and viscosity prevents forming another flow in a wedge shape to fill in, so the original stream sticks to the surface. And this means a pressure gradient again establishes that overcomes its inertia, this time with low pressure near the surface.
Bernoulli's principle tells us the velocity, again somewhat counter-intuitively⁵, increases, but that is again just a side-effect; we already know the pressure is reduced.


Second video
Last, the experiment in the second video relies on the fact that the air is expanding in multiple directions, so the cross-section available to it increases⁶.
According to the above, the velocity on the outer edge will be such that the static pressure matches ambient. But before it gets there, it has to squeeze through the still much smaller area near where the hose is connected. Since the same volume⁷ of air needs to get through both per second (due to conservation of mass), and to do that, it must move faster. And since it moves faster, its static pressure is lower, and this creates the pressure differential that pulls the plate towards the nozzle.
This is the only of the experiments that is actually demonstrating Bernoulli's principle.
Curvature v.s. speed
You see some of the cases are governed by one and some by the other. Fluid dynamics is extremely complex and difficult to calculate – the “easy solvability” or Navier-Stokes equations (that describe fluid dynamics; Bernoulli's equation is included in the set) is famous.
Generally, the curvature works in most situations, but watch out for aerodynamic stall (when the angle is too steep for viscosity to keep the fluid flowing ‘orderly’), while velocity only works when you have control over it, which is generally just in closed pipes.

¹ Bernoulli's equation simply expresses the internal energy of a fluid. If you do work on it you are adding energy, so that energy has to be added in the equation.
² Potential energy term omitted for brevity.
³ Dynamics of jet and rocket nozzles is much more complicated, but at the low velocities involved it holds pretty well.
⁴ It is counter-intuitive because it looks like the air has to move through less space, but since there is no opposite wall, it is free to expand as it suits it.
⁵ This is counter-intuitive because it looks like the air needs to expand to more space, but again there is no other wall, so it can pull more air from far and wide to fill that space.
⁶ I am not completely sure this case does not involve some additional effects.
⁷ Actually the same mass, and to be accurate we should include the adiabatic expansion of air, but for the speeds involved air can be approximated as incompressible.