So I know that the formation of a supernova has been observed and that we have taken images of blackholes, however, has the formation of a blackhole ever been observed. How do we observe it?
“We think that ‘The Cow’ is the formation of an accreting black hole or neutron star,” said Northwestern’s Raffaella Margutti, who led the research. “We know from theory that black holes and neutron stars form when a star dies, but we’ve never seen them right after they are born. Never.” ... Another team of astronomers, led by Paul Kuin from, an astrophysicist at University College London, came to a different conclusion. They think that the Cow is a star that’s been ripped apart in what’s called a “tidal disruption event.” Information on that here.
There are only 25 Stellar black holes and candidates.
If 'The Cow' was a dwarf star being consumed by a blackhole then the most likely occurrence that has been observed is N6946-BH1. "Candidates outside our galaxy come from gravitational wave detections. The disappearance of N6946-BH1 following a failed supernova in NGC 6946 may have resulted in the formation of a black hole." The list of other ones is here and for information on the disappearance of N6946-BH1 here.