How seriously should we take Gandalf when he tells Frodo that Sauron though the ring was destroyed?

In chapter 2 Gandalf says this to Frodo.

‘And this is the dreadful chance, Frodo. He believed that the One had perished; that the Elves had destroyed it, as should have been done. But he knows now that it has not perished, that it has been found. So he is seeking it, seeking it, and all his thought is bent on it. It is his great hope and our great fear.’

Over the years I've seen some people question how much we should trust Gandalf on this statement. It seems like he's making speculations onto Sauron's state of mind.

Unfortunately Gandalf never tells us where he is getting this information from or why he thinks this is the case.

To back it up Sauron never searched for the ring before he came across Gollum someone who he recognised was touched by the ring.

If Gandalf is correct then this raises a lot of questions. Why does Sauron now think the ring being destroyed would kill him and why does he think no one will be capable of destroying it if he already thought it was destroyed previously.