[stinos]

looking literally for nothing in particular

That's not what I said. My last question covers this exactly: are there metrics other than 'conditions like we know them' which can be used? Maybe the answer is just 'none that we know of', again: no idea, and yes then one cannot look for it. But here on earth we can distinguish between a rock and a cell based on various metrics. They way they reflect light is perhaps different enough to tell that one is a relatively simple solid consisting of chemical bonds which are all alike, whereas the other one isn't. Or processes in the cell make the atmosphere slightly different. Now suppose some other lifeform also consists of cells but instead of water-based they use something else which happens to be liquid at 200 degrees Celcius. A rock can still look like a rock at that temperature and maybe won't alter atmosphere. Maybe something living would?

Also I don’t non-carbon/water lifeforms are at all compatible with our understanding of biology and chemistry?

It's not because we cannot understand it that we cannot observe it. In fact that's usually how it goes: first observ, then understand. Isn't that basically what we're doing already with a lot of telescopes/wide band radiometry/... ? Looking for things without understanding how they can exist or where they came from (the OMG particle etc)