How do physics notions of fluid dynamics relate to pressure gradients in circulation?
As far as we know so far, biology isn't able to break any laws of physics.
However, biology isn't passive: biological systems react to changing environments to maintain some level of homeostasis. Arguably this is one of the defining characteristics of life.
If you narrow the aorta, you will always get compensatory changes. Ultimately, the circulatory system is tasked with delivering sufficient blood to the body. It might be a bit of an oversimplification, but let's assume that blood flow stays constant, because flow is a good measure of the ability of circulatory system to deliver enough oxygen/nutrients to the periphery.
Blood flow is pulsatile, which also adds some challenges in understanding things simply, but let's simplify and think in terms of mean pressures. Again, this is wrong, but it's not terrible, kind of like when in a physics class you discuss a &quot;uniform spherical cow&quot; or something like that.
We can start with an equation you mentioned:
ΔP=Q*R
You write:

In this condition the radius of the blood vessel decreases which should mean that pressure decreases too

This is false. If we keep flow (Q) constant, but R increases due to a constriction, then ΔP, the change in pressure, must increase.
Consider:
ΔPaorta=Q*Raorta
If Q stays constant, but R (resistance) increases due to the decreased radius, then ΔPaorta must increase: there is a larger pressure drop. Perhaps you've confused the larger change in pressure with a &quot;decrease in pressure&quot; because there is this larger pressure drop?
Consider also that we can consider the rest of the parallel vasculature (all branches off the proximal aorta) in series with the aorta. If we think of the vasculature after the aorta as:
ΔPdistal=Q*Rdistal
then you can think of the whole system as:
(ΔPaorta + ΔPdistal) = Q*(Raorta + Rdistal)
If only the aorta is constricted and the distal vasculature keeps the same pressure and flow, then ΔPdistal must also not change. Therefore, the total pressure drop (equal to the difference in pressure between the aorta and great veins, the sum ΔPaorta + ΔPdistal) will be larger when ΔPaorta increases.

As far as Bernoulli:

This theorem and the fact that velocity has to increase to maintain a stable flow through the coarctation should mean that the pressure gradient drops. Moreover in every textbook I've found it is said that tension on the aortic wall increases too but this seems even more counterintuitive

Due to Bernoulli, if you go from large (A), to small (B), to large (C) diameter in some vessel, yes, you will have less outward pressure in the segment (B). You will also always have decreasing energy from A to B to C. However, think about what we were just talking about: if you want to keep the perfusion of the rest of the vasculature constant, that means you have to keep the energy at C (interchangeable with pressure in this context) constant, despite the constriction. You shouldn't be thinking about A B and C here when comparing a vessel with and without stenosis, you have to think about the non-stenosed case where you have large (X), large (Y), large (Z). In this case, you still have decreasing energy from X to Y to Z, but without the stenosis, you don't lose as much going through segment &quot;Y&quot;. It is segment A that requires more energy/pressure/tension on the vascular wall compared to segment X.
There's some simplification here regarding vascular compliance, non-Newtonian fluids, and vascular permeability but these can be mostly ignored for these purposes. I think this website will help you a lot:
https://www.cvphysiology.com/Hemodynamics/H001
especially
https://www.cvphysiology.com/Hemodynamics/H012
for the part about Bernoulli's principle.