Sol does have three habitable planets. Plus some moons, at a push.
Habitability isn't a Boolean. It's hugely dependent on history, context, and resources.
The more Boolean distinction doesn't have a name - but if it did, it would be something like Stable Evolutionary Potential.
Mars and Venus both fail on that. The moons fail on it now, but may pass when the Sun turns into a red giant.
The Earth has offered it for long time, with some uncertainty about the near future.
There's no reliable way to distinguish SEP at a distance. But noting that a star has planets in its habitable zone and making some estimate of how many planets in stable systems are likely to offer SEP is a decent start.
I highly recommend the book The Equations of Life: How Physics Shapes Evolution[0] . While it's be foolhardy to rule out other dramatically different forms of life, there are only so many candidates in the periodic table and only so many of those in common concentrations throughout the universe. The universal laws of physics that continually converge on the same solutions on Earth, and the fact that life has apparently failed to succeed even on nearby planets (perhaps at all, and certainly not advanced life) with different conditions suggests that it's at least unlikely to find life thriving at far different temperatures (atoms just don't hold together or move enough) or bases (I wouldn't completely rule out silicon, either, but the author makes a good case that carbon is far more likely)
Why does life have to be chemical as we know it? Why can't a massive galactic-scale lifeform exist upon gravitational waves, radioactive particles, or even dark matter or things we don't know?
I agree with your general idea, that perhaps life exists in non-chemical ways, but a galactic scale life form would be tricky for a ton of reasons - just one would be inter-organism communication.
The Milky Way is a pretty average galaxy and it's 100,000 light years in diameter. In humans, if inter-hemispheric signals takes 3ms you can achieve roughly 40hz "synchronic activity". Let's say (and this is a massive simplification) that the inverse of the maximum inter-brain delay is ten times the "clock speed" of the brain. That would give a human that lives 80 years over 100 billion clock cycles in a life, and a galactic brain that communicates at light speed (so 3e-13 hz "clock speed") only 9467 clock cycles in 1 billion years.
So one single human life would have ten million times more "clock cycles" than a billion years of this galactic life-form existing. Or, the galactic life form would have about 3 minutes and 55 seconds worth of "normal" human thought, from the moment it's born until one billion years later. I know human babies certainly don't do a lot in their first 3 minutes and 55 seconds.
Or, for a simpler example: say a massive star goes supernova at one end of the "brain", damaging it and requiring resources from the other side. It'll be a minimum of 200,000 years before that section gets repaired.
Life isn't something that's easy to define because literally everything exhibits patterns of life to some degree (in fact, you could definitely argue that the concept of life is an arbitrary, fictional distinction made to make our lives easier). For example, we find that cities, states, and empires look "alive" at a macroscopic level, with cars and roads forming the circulatory system to deliver much needed nutrients to far corners of the respective territories; we often give anthropomorphic characteristics to planets (Mother Earth) and stars.
When we search for life, we're probably looking for something very similar to us, something we can interact with and befriend.
Some of the qualities of life is that it needs to: (1) be able to grow, (2) be able to reproduce (3) have hereditary traits.
I'll grant that there are probably galactic-scale patterns of light and gravity. My guess is that the amount of noise would make it impossible for any "life" to form. The unspecified type of wave would have to have an ability to store information in such a way that it would change the behavior of the waves.
As a tangent, these requirements of life is what makes the RNA world hypothesis so compelling. RNA is able to both store information _and_ act as an enzyme. 2-fer!
Evolution, because no other phenomenon can drive the required complexity to reach 'life'. Natural selection works by inheritance and mutation. Things that can create copies of themselves with mutations that allow selection to act on, this list is short.
The question is, what kind of life do we know how to recognize? What kind of life definitely is possible, and what kind is just speculation? In other words: where should we look first?
The answer is: carbon rich, watery life. Coming up with biosignatures for ourselves is hard enough, coming up with a biosignature for a galactic nebula is unbelievably harder because we have no examples. Extrapolating from one example is much easier than from nothing at all.
