pressure - $P=F/A$ and $P=rho*g*h$ give different answers

I have searched for this, and while I have found questions that brush on the same issue, my question wasn't fully adressed by them. This one, namely, is very similar, but I still don't totally get it.

So, let us have two containers, both of them have a volume of liquid $V$, bottom area $A$ and filled with the same fluid of density $\rho$. One of hem has a liquid column of height $h$ and the other one $H>h$.

According to hydrostatics, the pressure at the bottom of the containers is the following

$P1=\rho*g*h$

$P2=\rho*g*H$

$P2>P1$

On the other hand, we could look at the fluid as if all of its weight was being supported by the bottom wall (I realized that this might be my mistake while I was typing this. I'm gonna finish anyway to get some input from people who understand the issue better.)

That assumption would lead us to:

$P1=\rho*V*g/A$

$P2=\rho*V*g/A$

$P2=P1$

Which is inconsistent with reality.

I arrived at this problem by imagining what would happen if we put a very thin and long straw filled with fluid on top of a container, which would make the pressure $P2=\rho*g*H$ go really high by increasing $H$, which would mean that we could make any container fail by excessive stress if we put a long enough straw on top of it, which is absurd. In this case, the second analysis kinda makes more sense because if you don't increase the volume, you basically also don't increase the pressure, but I know this has to be wrong since pressure does depend on height of fluid column.

I guess this is kind of two questions in one, as I have one question that asks for correction on the concepts I used to calculate something and another one which is the question about how the absurd situation doesn't happen. If you prefer to focus on "one question", please focus on the second one, since it is the one that I feel less able to tackle myself.

FINAL ANSWER: I have been convinced. I thought the situation on the following video was absurd/impossible, and it isn't. My mind is settled. Thanks for your answers people!

https://www.youtube.com/watch?v=EJHrr21UvY8

Answer

"we could make any container fail by excessive stress if we put a long enough straw on top of it, which is absurd."

Absurd it might seem, but it's what happens. Barrels have been burst by putting tall thin pipes into their tops and filling with water.

You correctly diagnosed your mistake earlier on. When containers have sides that aren't vertical, these sides exert on the liquid forces that have a vertical component, either up or down according to whether the container is becoming broader or narrower as we go upwards. The thing to remember is that a liquid at rest exerts on a surface a force at right angles to the surface. The surface exerts an equal and opposite force on the liquid.

My favourite derivation of $p=h\ \rho\ g$ equates the work done pushing a piston at depth $h$ against the liquid to the gravitational PE acquired by the displaced fluid as it (effectively) rises to the top of the liquid. A bonus of this method is that it shows the pressure to be the same whatever the angle of the surface that the liquid is pushing against.