Please don’t trot out that tired, pedantic trope.
A republic form of government is a subset of democracy, not a sui generis construction.
Yet you denigrate the meaning of the real difference in that distinction. In no way, shape or form is a mob-rule democracy the same as a republic governed by laws. While true that republic has aspects of democracy via representation by legislators, it patently cannot overrule (in theory) established laws for the protection of individual rights.
Your insistence in trying to equate the two without the very clear distinction is tired, pedantic trope also.