You say, " Extraterrestrial life would be intrinsically defined by a different environment, and therefore might develop different senses based upon different paradigm (or at least different parameters)."

I could understand parameters being different, maybe E.T. could develop vision capable of seeing x-rays or infrared wave length, but most else would not seem to be much different.

Senses: (to say the least)
Touch/feeling - a sensation recognizing things of kinetic energy, heat, motion or friction.

Vision - capabilities of recieving light a small spectrum of electromagnetic radiation, to which brain interprets(to say the least).

Hearing - kinetic energy sense detecting a range of decibels. Parameters of a different range is understood, dogs hear things people dont.

Smell - recieved chemical reactions in near by atmosphere (smelling the moon would mean moon dust would have to enter the nose, cannot smell moon millions of miles away).

Taste - following simular to smell but a different reception for different chemicals.

You make a good point and question but my first thought was "A netflix series".

Our senses are not the only limitation, just distance alone is enough, to detect the signs of life, which is a very tiny thing, as far as we know, (Life on earth is just a couple of miles thick, at most, film, on the surface of a planet, which as a whole, makes up less than a thousanth of one percent of the solar system. ) at the distance of other stars, would be practically impossible even if it was exactly like ours.

The distances are such that it is likely we could only see the emissions from very advanced technological cultures, which may be far less common than life itself, and may be short lived anyway. Technology may quickly lead to self destruction, or many life forms which develop it, may just abandon it. The only other things which could be detected are things like oxygen in the atmosphere of exo-planets, but that requires very catching them at very rare moments when light passes though those atmospheres as they pass across the face of stars, and needs very high quality detection.