They borrowed about the disappearing Sauron with the ring. When will we read the primary sources so that we don’t ask stupid questions? Answer for the last time.
First, the Ring is “reasonable,” has its will and makes its decisions. Secondly, the Ring gave each one the measure of supremacy which he imagined (unconsciously, himself) and which he was able to endure. For Gorlum-Smeagul, omnipotence was conceived as an opportunity to look after everyone while remaining invisible, and to do the ugliness of a little bit. For Bilbo, the only desire at the time of finding and first use of the Ring was not to be eaten by Gorloum and to get out of the caves. Frodo knew how the Ring worked in Bilbo, and the Ring could not deceive expectations. It did not affect Tom Bombadil at all, since Tom was endowed with all the possible and desirable powers for himself (a simple analogy: he was pumped to the maximum level))). Furthermore, if the Ring had reached Boromir, he would have become the invincible warrior, the most powerful in all the Middle Earth and all that, but most likely would have become excessively cruel and conquered and killed everything that moves.
And Sauron just... well... wanted to be the Strongest. Invisibility has nothing to do with him.
Now is understandable?