what exactly was he supposed to do if he didn’t have enough senators to get it passed without Manchin’s support?
Eh, I think it is fairly moot as Biden would have to have confidence that progressive policy (especially regarding climate change) has popular support and he would not be blamed (or even hurt) by pushing for their passage.
Manchin and Biden would almost certainly have stood to benefit from having passed BBB in the first place. Before that they and the Democratic Party would have had a net benefit passing the Green New Deal.