Thanks to all the commentators for pointing out partial answers.
I dare say I found the reference which answers why at the same power setting there exists a point (at some AoA) at which the vector of speed angle (= angle of climb/descent) starts reacting opposite to stick movements (pull stick => less climb angle / steeper descent).
It is power curve.

Power curve is best explained here from where I bring a citation (Paragraph 7.8):
The airplane is trimmed for a definite angle of attack, and hence a
definite airspeed at 1 G. The yoke is part of the angle-of-attack
control system. Pulling back on the yoke will always make you slow
down.
If you are on the front side of the power curve and if you don’t mind
airspeed excursions, you can use the yoke as a convenient, sneaky way
to control altitude. This is because airspeed is linked to altitude
via the law of the roller-coaster and via the power curve.
Warning: just because this works OK 99% of the time, don’t get the
idea that it works all of the time. Bad habits are easy to learn and
hard to unlearn. Do not get the idea that pulling back on the yoke
always makes the airplane go up. On the back side of the power curve,
it doesn’t work — and might kill you. In critical situations
(including approach and departure), you simply must control the
airspeed using the yoke and trim.
Power curve contains an implicit dependence of AoA (since AoA is roughly airspeed):

- So when I am at full thrust climb and I start pulling, I increase AoA and move right to left on the power curve — increasing agle of climb. At some point for the reasons of fastly increasing drag coefficient and slowly increasing lift coefficient (see lift coeffcient and dreag coefficient curves) it stops increasing angle of climb. I'm in this point (which is $V_X$ by the way, see the link):

- Exactly the same occurs in descent. In idle thrust regime, I start pulling stick back more and more and I move right to left on the power curve, descending less steeply.But after passing some speed (which is not $V_X$ but rather close $V_{L/D}$) I start descending steeper:

- As explained in 1 and 2, the points on the power curve at which this happens are $V_X$ and $V_{L/D}$.