Apparently, I say this because I am old, likewise yerdad, who is also old, will say this from time to time. We had no idea it is such a new word that is primarily used by old people.
As you gathered from the context, it means that things are essentially okey-dokey and somewhat better than comme ci comme ça, which is old-people speak for, as you say, “meh.”
According to Miriam Webster, tap dancer Bill “Bojangles” Robinson claimed to have invented the word copacetic as a boy in Richmond, Virginia. Others dispute this, but I think Bojangles should get credit, mainly because I like saying Bojangles.
The song, Mr. Bojangles, has nothing to do with Bill Robinson directly, but is supposedly based on the story of a man who was using the name to disguise his identity in jail. Supposedly. (I google so you don’t have to!!)
I have dived down a long and twisty internet rabbit hole to try to locate a recording of William Shatner singing the song, sadly it has been destroyed from orbit. I did, however, find a playlist with twenty-eight versions of the song.
You may want to bookmark this for a time when you have a hostage situation and things are not entirely copacetic: 28 versions of “Mr. Bojangles” for some reason.