Common-Source Amplifier
For small signal, I would recommend thinking of this simply as two parallel (but complementary) transconductors (or CS amplifiers if you want to look at it like that). If I redraw it, perhaps it makes it more obvious:

In a small signal sense, a NMOS CS amplifier is no different to a PMOS CS amplifier, so a parallel connection will simply give you a combined transconductor. This is exactly the same situation if you instead decide to combine two NMOS CS amplifiers or two PMOS CS amplifiers in parallel.  Ofcourse, the behaviour of these arrangements are going to be totally different in a large signal sense.
Some of your explanations seem to be trying to understand the amplification by thinking of how the operating points of the PMOS and NMOS will change for the same input signal. Do not do this, as this is exactly what you avoid in small signal analysis. Assume the signals are small enough to not change the operating points and then proceed to just think of these as transconductors.
If you instead want to understand how this would behave as an inverter (so large signal characteristics), then go down the rabbit hole of imagining how the signal would change the operating points and the resulting transfer curve that would emerge.