You may be confused about the historic origin of “republic,” perhaps. It comes from the Latin res publica and more or less means “people’s state.” It means that ultimate sovereignty lies with the people. The state belongs to the people, is created by them, is ultimately answerable to them.
This was kind of an obvious thing to the Romans, but in the period that followed them it fell very much out of favor. To the Medieval mind, sovereignty rested with the prince, who was ultimately answerable only to God. He might certainly ask the people their wishes, and he was charged with their welfare, so that, in theory, if he did not do what was best for the people – which is not necessarily that for which they asked – then God would smite his sorry ass. That threat may bring a smile to your face but in 1100 AD the threat of eternal damnation of your soul for doing wrong was deeply frightening to people.
The philosophical Christian king of the Middle Ages felt that a republic was readily prone to political gamesmanship, corruption and decadence, and the oppression of minorities, because the only constraint on the behaviour of its government was “what the majority wanted.” It had been readily observed that rabble rousing hucksters were capable of leading the people into grave error, and that tying morality to “what most people say is right right now” inevitably led to a shallow and evanescent public morality, and of course that if the majority is always right and gets whatever it wants then minorities are completely at its mercy and can, and would, be savagely oppressed or exploited. Hence, the foundation of a just government was considered to be the appropriate fear and love of God and His justice, and the earthly prince had better do his best to approach that platonic ideal. For example, the prince could not allow minorities to be persecuted by a majority, no matter how overwhelming the vote for it, because that was contradictory to the commandments of God – and The Big Guy was sovereign, ultimately, not any temporary majority of fallible mortals.
Of course, how well that worked in practice is a matter of debate. A debate which formed a major part of the Reformation and Renaissance. Approaching the foundation of the United States and the general liberalization of the West, you still had a division in thought, between those who felt ultimate sovereignty rested with God, and the prince was his regent, and those who felt it was all a crock and ultimate sovereignty rested with the people.
The Founders of the US were well aware of the practical difficulties of founding a country based on the principle that God was its ultimate ruler, namely, how do we know what the Big Guy has to say on day-to-day matters? But conversely, they were also well aware of the tendencies of democracies to tear themselves to pieces and to oppress minorities. So what they did is invent this pseudo-God, “The People”, who are something like a platonic ideal of real people (us), and who are ultimately sovereign. They are the authority from which the government draws its power. But They are not quite us, if you know what I mean. When we – real ordinary people – express our opinion, government is not expected to instantly do what we say. Because The People are not exactly represented by any momentary majority of the people now alive. The People are something like a time- and space-average over real people. That is, our behaviour as real people, taken over a long enough span (possibly more than one generation) and over enough individual circumstances, approaches the behaviour of The People, and is ultimately sovereign.
The Founders put in a bunch of restraints on what the people can do (indirect election of the President and Senate, federalism, checks and balances, the Bill of Rights, three branches of government deliberately left co-equal) – so that foolishness would be restrained until the time-averaged wisdom of The People emerged instead. This is what you’re calling “a republic” – all those checks on the will of the majority. But that is a modern Western (typically American) back-construction, it is not the original meaning of the word, nor how it’s generally used elsewhere. Those features are more often called being a constitutional representative democracy (or republic, doesn’t matter which), which just describes some of the typical constraints put in to prevent the people from deviating too wildly from what The People want to do. But those constraints can also exist in systems in which the ultimate sovereignty rests, at least in principle, with a prince answerable only to God, such as England, which is (in the original meaning) therefore not a republic.