It’s a democracy just because it says it’s a democracy ?
No, your criteria for a democracy needs a “higher bar”
It used to be (might still be), that in order to join he United Nations, a country had to be a democracy. Spain, under General Franco, famously declared that it was not a democracy, but a military dictatorship. Accordingly Spain was refused entry to the UN until after Franco died.
So ALL countries declare themselves to be a democracy in order to gain membership of the UN.
A democracy is a state that’s governed by democratic principles - ie: in accordance to the will of the people (at least in the long term).
eg: the USA is an obvious democracy.