What did we learn by detecting a gravitational wave?
We learned that LIGO works.
When making a new scientific instrument, there's always the chance that some unforeseen problems will make that instrument work poorer than expected. For example, the fuzzy images first sent back by Hubble, the supposedly faster-than-light neutrinos; the list of scientific instruments that did not work according to expectations goes on and on.
Suppose it hadn't worked, that it ran for months and then years without seeing anything but noise. This is exactly what happened with the initial version of LIGO, which ran from 2002 to 2010 without seeing a thing. Nobody took those initial negative results as disproving general relativity. They instead took it as a sign that they needed to improve sensitivity, and by a good amount. Suppose that the improved LIGO hadn't worked. This, too, would not have been taken as a sign that general relativity was wrong. It would instead have been taken as a sign that LIGO was yet another scientific instrument that didn't pan out.
That's not what happened this time around. It worked, and it yielded a positive result much quicker than expected. The concept is now known to be sound. What we have learned is that there's much more to be done. More detectors around the world would be nice. Further improvements to sensitivity and directionality would be very nice. A set of gravitational standard candles would be very, very nice.
There's a solid wall, the surface of last scattering, beyond which even the best telescopes based on electromagnetic phenomena cannot see. Something else is needed to see beyond that surface. Perhaps neutrino detectors, but detecting high energy neutrinos is very hard. Detecting massively redshifted neutrinos is far, far beyond the capabilities of current science. The only other option (so far) is gravitation.
Now that we know LIGO works, LIGO (or something like it) is the best bet to being able to see beyond the surface of last scattering. And then we will learn something truly new.