Well, let’s just dive right in and second-guess the author, shall we?.
It ought to go without stating but I’ll state it first: There is no other way to supply an authoritative, conclusive response to this concern. But let’s start by differentiating in between Gandalf and J.R.R. Tolkien. Tolkien himself made a similar point in Letter No. 153 (composed in reply to Peter Hastings, who thought Tolkien was being inconsistent):.
… Treebeard is a character in my story, not me; and though he has a fantastic memory and some earthy knowledge, he is not one of the Wise, and there is quite a lot he does unknown or understand …
Of course, Gandalf is not Treebeard; in fact, Gandalf is among the Wise, but even so his understanding has limitations and his knowledge and insight in some cases fail. He is not best nor omniscient (both attributes Tolkien reserved just for God).
Gandalf informed Frodo exactly what he had actually deduced of Sauron’s thought. It is rational to presume that Sauron thought the Ring damaged due to the fact that A) he was weaker than he had been when he possessed the Ring and B) he did not begin searching for the Ring up until Gollum was captured and revealed it still existed.
Isildur, Elrond, and the One Ring.
Isildur, Elrond, and the One Ring: Did Tolkien oppose himself when Gandalf said the Elves could not destroy the Ring and yet Sauron thought they had?
Exactly what I believe we can presume from these obvious discrepancies in the text is that Sauron, reconstituting himself without the Ring, could discover no sign that it still existed (even though Tolkien as author mused in his personal notes that Sauron was still “in relationship” with the Ring). What else should one assume if there are no plaintiffs to the Ring and it is not with the maker? If Gandalf’s deduction is correct then Sauron overestimated the knowledge and power of the Elves, which is not necessarily contradicted by the later remarks in the book.
After all, upon Sauron’s death on the slopes of Mount Doom the Elves (and Dunedain) had control over Mordor and Mount Doom itself. At the time they for that reason had the methods to damage the Ring. Isildur’s inability to do the deed was what saved Sauron but after he re-incarnated himself Sauron had no concept of exactly what occurred. Isildur was dead. Had he kept the Ring it would, most likely, have extended his life and ultimately turned him into a wraith. Nobody appeared with the Ring in their belongings, either as a living being or a wraith.
Mordor stayed in Gondor’s control until the Great Plague of 1636. Hence, Gondor had the capability to destroy the Ring for over 1600 years, and Sauron created a brand-new body for himself sometime in the 11th century of the Third Age. He did not sense or find the Ring during those centuries, not amongst his servants nor amongst his enemies. For this reason, what else should he have concluded except that the Ring had been ruined? He eventually discovered that was not so, and just after he had gone back to Mordor.
With three thousand years to ponder the implications of the Ring’s survival Elrond, Gandalf, and others with complete understanding of the Ring’s history and purpose might have been more sure of what would occur when the Ring was destroyed than Sauron himself. While (prior to he questioned Gollum) Sauron might have feared that the Ring was gone he was still able to incarnate himself. For that reason his reasoning was flawed due to the fact that of his lack of knowledge. But once he seized control of Mordor once again there was not any method the Elves and their allies could destroy the Ring securely. And when Sauron discovered the Ring still existed he also found why it had actually been lost for three thousand years. He therefore fell back upon the belief that somebody with higher ambition than Gollum possessed would ultimately wish to utilize it.
I think Gandalf’s reasoning stands up to analysis here. Each of the points you raise stands but in a various context. As the characters’ understanding of the real facts of the circumstance altered their assessments changed. Also, Gandalf and other members of the White Council had been tricked by Saruman, who was the first to understand that the Ring was still somewhere in Middle-earth. He told them it had rolled down the Anduin and entered into the Sea, lost forever. He could not get away with saying it had been destroyed due to the fact that they would have known it could not be destroyed other than in Mordor, and nobody ever dropped it into the Cracks of Doom.
Hence, the Wise understood Sauron was still able to re-embody himself due to the fact that the Ring still existed, but they believed it might not be found once again. Sauron thought he was strong enough to take shape again without the Ring but he thought that the Ring had actually been damaged. After Sauron learned about the Ring from Gollum his knowledge of the facts changed. When Gandalf validated that Bilbo’s ring was certainly the One Ring his understanding of the facts changed too. Now the possibility of un-making the Ring presented itself to Gandalf and the possibility of someone else declaring the Ring presented itself to Sauron. So their thoughts entered various instructions as they tried to second-guess each other. Gandalf understood there was only one place the Ring might be destroyed and Sauron understood it was only a matter of time before someone aimed to take the Ring.
So I think it’s reasonable to say that when he understood the Ring had not been destroyed Sauron became more persuaded than ever that nobody would ever try to ruin it. After all, in 3 thousand years no one had been able to do that.