If you wanted to get particularly philosophical, everything is observed by its effect on other things.

That's right, observations were made that do not fit with our current understanding of physics (equations). That means our understanding is wrong. So instead of assuming the equations are wrong physicists invented an invisible type of matter. That is not science. Dark matter is nothing more than modern day aether.

Black holes are made of regular matter not dark matter because they interact with electromagnetic waves.

They’ve been both predicted and observed. Dark matter is a conjectural solution for an anomaly in the rotational speed of galaxies across their discs. In my opinion, it’s almost certainly a bodge, and if the W boson has a different mass to that expected it could account for what we call dark matter, as the implications go far beyond just the additional mass - if the mass is off, then perhaps the nature of the weak force is misunderstood - for instance, perhaps the mass variance is driven by a hidden variable, and that in turn could account for what we regard as “dark” phenomena.