I assume you’ve focused on the definitional fact that constitutional monarchies are not “republics.” This is of minimal interest to most of us, but if you want to discuss it please start a new thread. It certainly has no relevance whatsoever to OP or the Economist’s rankings he cites.
(FWIW, eight of the eleven highest-rated democracies are constitutional monarchies.)
To confuse matters more, some describe the Westminster system as being a ‘crowned republic’.
So are “gay” and “happy”, but tell that to Matthew Shepard.
I was simply responding to your suggestion that democracies and republics are synonymous.
I wrote “almost synonymous”; and intended to contrast with another poster’s bafflingly absurd
… Do you prefer the latter to my “almost synonymous”? Whatever.