But surely even if Manchin did back down, and vote to abolish the filibuster, there wouldn't be a filibuster proof majority in the Senate. And that would still be the case if the DC and Puerto Rico were admitted as States, and the Democrats had four more Senators.

Pretty foolproof block. Rather analogous to the block on electoral reform in the UK to get some kind of electoral reform, which is that by definition any government is likely to in power only because it was elected by the present system.