The 'area theorem' they are referring to was by Bekenstein and others, not Hawking. It's basically the equivalent of the second law of thermodynamics for black holes (dA/dt>=0 instead of dS/dt>=0). Hawking's insight was that this formula was wrong and the area could decrease due to radiation.
But it is a fascinating area of research. I never expected that we could measure gravitational waves in our life time.
I mean I'm no astrophysicist, I like the "pop sci" bits, but when I look closer I'm seeing a lot of small numbers and statistics that imply something - e.g. exoplanets based on minute wobbles and brightness variations, water on said exoplanets based on spectrography. It's theories based on tiny but statistically significant data.
The pop sci then comes in and makes statements like "second Earth found!11", which is like, whoa hold on, when you look closer all they found is a wobble or dimness variation that kind of implies there might be a planet at a certain distance from its host star.
Anyway I don't dispute the findings or that there are exoplanets or whatever, I'm just impressed that they are able to make confident claims on what little information we can receive from here.
For example, we know more about the chemical composition of other galaxies than we know about the centre of the earth. Just because we can infer so much from their light spectrum.
(For empirical information about the centre of the earth, we are basically limited to seismic data and perhaps the magnetic field and bumps in gravity?)
We barely can resolve largest and closest exoplanets into a few pixels.
For now...
This also requires a helluva lot of delta-V from the telescope to realign with another planet.
Then they combine all that info to come up with cohesive theories. LIGO just by itself would be almost useless.
The minute wobbles may be tiny, but they can plot a curve of those wobbles and see very clearly that it changes in a certain way that can only be caused by a planet (or something spherical and with a certain mass). If there was a competing theory of how you can get this exact curve in some other way, I am sure we would consider them as alternative possibilities and not be able to tell them apart, but as far as I know, there isn't any competing theories at all... so we can have very high confidence there's a planet there.
Regarding water detection: yeah, spectrography is just mind blowing, but again, given what we know, there's just nothing that could justify believing that when you detect radiation that fit exactly what you would expect from water molecules, that it could be something else instead... unless you come up with a convincing "something else", your only option is to conclude that the detection is accurate, otherwise you would need to stay open to the possibility of absolutely everything possibly having alternative explanations we haven't thought of yet (though every now and then, that indeed can happen and we need to adjust all our theories that are based on the changed body of knowledge), and progress would not be possible in any area (you need to accept something before you can build on top of it).
However, Wobbles and Transit photometry are done over time and plot trends which definitively show that something with a certain mass is orbiting with a certain period around the star. There isn't really anything else it could be except an exoplanet, unless our understanding of how physics works was way off, which we know it isn't.
as for Spectrography brabel sums it up in their comment very well.
Also, Venus must have a big enough sulfur line in the atmosphere, which is absent in Earth atmosphere.
Probably Mars and Earth could be considered close, save for the oxygen line, but not Venus and Earth,
Even though from a theoretical perspective it should be way easier and more reasonable to detect particular molecules on distant planets via spectroscopy compared than to detect things on the mind-blowingly minuscule scale of gravitational waves, I think distant spectroscopy might actually be more prone to error, or at least more prone to false positives.
Just speculating since I have zero expertise in this area, but part of it may be because light from all sorts of sources is reaching us all the time, while gravitational waves significant enough to be feasibly detected pretty much only come from the top percentile of the most energetic events in the universe.
I think if you can discern a gravitational wave-induced spacetime wobble at least once and infer the motion that could've caused it (e.g. black holes/neutron stars merging) and see it matches theoretical expectations, you may continue to have a lot of false negatives, but you probably aren't at high risk of future false positives.
Whereas with spectroscopy, there seem to be a lot of things that can cause both false positives and false negatives even if you do have many prior detections that you believe are accurate. For spectroscopy, both error rates should go down over time as technology and techniques improve, but it seems like it may potentially be an inherently more "murky" observation technique, even if it's far simpler and far less expensive than gravitational wave detection.
(Someone please correct me if I'm wrong about any of this, because there's a pretty good chance I am.)