Yes. it’s a republic. It’s a representative democracy.
Many republics are dictatorships. Several non-republics are representative democracies.
Great Britain is a representative democracy, but is a monarchy.
Iran is a representative democracy but is a theocracy.
You need to learn the difference between how laws are made and the basis of the laws.
The founders did not use the word democracy intentionally. Democracy, like socialism, fails every time it is tried.