Serious question: Would he really have that much of an impact?
There was zero chance that West Virginia was ever going to vote for Biden anyway. None. So it's not like him being able to win his home state is going to cost Biden any votes. If anything, he'd cost Trump some votes. The way I look at it is either he's going to win a state that Biden never had a chance of winning in the first place, he's going to lose to both Biden and Trump and accomplish nothing, or he'll win the state so Trump doesn't get the votes and then win precisely 0 other states, again hurting Trump by costing him W. Va's 4 Electoral College votes. Strictly looking at West Virginia, Manchin being in the race either has no effect on Biden or could actually help Biden by sabotaging West Virginia enough to tilt it to him.
He's only going to matter in swing states, and even then I think his impact would be limited. Biden would lose the right-leaning swing voters who might hold their noses and vote for Manchin because Trump is just that bad, but I think that population is extremely small. Left-leaning swing voters who are unsatisfied with Biden aren't going to vote for Manchin because they know that a vote for Manchin is essentially a vote for Trump, and I doubt there are too many people out there saying "I'd vote for any Democrat but Biden" or otherwise vote for Manchin knowing full well it's a de-facto vote for Trump. They may not like Biden, but anyone involved in politics enough to consider a third party candidade isn't going to vote for a third party candidate knowing full well that it could lead to Trump back in the White House.
I also don't think that he's simply all that popular outside of his home state. He comes off as your stereotypical old man yelling at a cloud, and has about as much of a personality as sandpaper. I can't see him being endearing enough to enough swing voters to get them to vote for him knowing full well his chances of making it are 0% and could lead to Trump's re-election. The biggest problem Dems have with Biden is his age, and a 75 year old Manchin isn't going to be considered the solution to that problem.
I think his impact is going to be extremely limited and look a lot scarier than it actually is.