Why leave a party where you control the agenda with your vote to become just one of 5-6 other squish “moderates”?
The reason to change, is that he would tip the balance of power to the Republicans if he cacused with Republicans.
He could get some nice committee chairmanships, among other benefits, if he switched. GOP would have to make him some offers. And if they didn’t follow thru, Manchin could always threaten to go back, and give Democrats control of the Senate again.