23 particular churches all united in one faith under one leader.
That is what “catholic” means.
What definition are you using?
Doesn't matter what definition I was using. What matters is what definition the Catholic-quoted source used in claims of "35,000 Christian denominations", why matching claims of 3,000 and 8,000 are given for Catholics by the same source using the same definition, and the implications of those numbers when applied to Catholics.