Kyrsten Sinema's pretty easy to figure out. She has no core beliefs; everything she does is for Sinema. So she's using Manchin as cover to get some pork for AZ and build maverick cred for if/when she decides to leave the Democratic brand in the dust. Simple enough. But Manchin...
Manchin seems like, at some point, to have become a true believer in the American Senate. And by that I mean he doesn't see it as a body whose job is to respond to crises and set law. He sees it as a place where the high priests of the American civic religion perform its rituals.
Imagine if someone not only took that Schoolhouse Rock about how a bill becomes a law very seriously, but thought the ritualized processes of the bill passing through Congress were far more important and integral to America than the bill itself. Then you might explain Joe Manchin
That Manchin's view of the Senate dovetails neatly with his own contingent personal power in it doesn't make this less likely an explanation, imo, but more. Easy to become a true believer if it also gives you everything you want. Ask the prosperity gospel preachers
Again, normal Senators finding themselves as this kind of pivot at any other time in US history just start asking for bribes, either directly or through pork. Manchin's been clear: he wants Mitch and Chuck to "sit down and figure it out," not black hole funding for a write-off