Everyone who can do something to prevent the reelection of Trump to the White House must mobilize in that endeavor. Biden has moved too far to the left to provide the strongest challenge to the former president, so it could be time to find someone more middle-of-the-road to challenge Trump. Such a campaign wouldn't spoil Biden's chances, it would save America from the clutches of authoritarianism.
A presidential run for a third party would be a foolish move by Manchin, who risks putting the country in jeopardy and tarnishing his own legacy. Biden and his policies are plenty bipartisan, and he's getting things done he promised to do. Biden deserves a second term, and Manchin should stay away from being associated with No Labels, which is a corporate-backed, problematic operation.
Joe Manchin is definitely right when he says that the Biden administration has been hijacked by the far left, but he doesn't seem to recognize that his entire party is overrun with extreme leftists. While Manchin's moderate approach as a red-state Democrat may appeal to some voters, he would likely just eat into Biden's fraying support base. A third-party run for Manchin would likely just increase Donald Trump's chances of returning to the White House.