But power doesn’t, right? Happy to be corrected (please, educate me!) but I think this is asymmetric, in practice.

That does not guarantee two-way communication. Pick-up patterns, resonance and filtering, power and local environment makes SNR highly asymmetrical.

Imagine you focus a high gain antenna dish A at an isotropic antenna B. A will almost exclusively hear B, but B will hear things from all directions, making it harder to single out A. Now, A could use their higher gain to scream louder at B - but that's not always a viable option, and could just peak the frontend of B if done wrong.

Different antennas and radio circuits have different selectivity, dictating how they react to nearby noise. A dedicated tranceiver station is often much more selective than consumer devices meant to handle many bands and protocols using a small set of multi-purpose antennas and with space requirements limiting room for radio frontends and filters.

The power rating of a dedicated transceiver station may also be quite a bit higher than that of a portable device, adding to the asymmetry.

There are also differences in atmospheric effects - primarily reflection and refraction - which for these wavelengths happen in the troposphere. With refraction happening closer to the ground (from the perspective of orbit), that makes for another SNR asymmetry.