>>213590735Sauron doesn't need to reclaim the ring, his victory is assured as things stand.
Gondor got saved by a couple of deux ex machina against a feeler force of Sauron's. An even bigger army was massing to besiege lorien and erebor because those are the places sauron assumed were going to be where the resistance came from.
Gandalf's keikaku with Pippin holding the palantir was to make Sauron strike out before his forces were marshaled so they could survive the first wave and buy frodo and sam some time.
Sauron was only worried about the one ring being claimed by someone who had a will stronger than his, which would unmake sauron, and corrupt whoever claimed the ring (gandalf, Galadriel, and MAYBE aragorn).
The ONLY winning play the good guys had was the destroy the ring.
Sauron wasn't so worried about this because he KNEW it would be impossible for anyone to willingly destroy the ring. It had enough will and agency, and the closer it gets to Mt. Doom the stronger that influence becomes.
Frodo, Sam, and Gollum only manage to destroy the ring because events were engineered to create a situation where the ring is forced to destroy itself.
By the time Sauron realizes what happened its too late to do anything and "the magnitude of his folly was laid bare."