You seem to assume I think Biden is in any way capable of motivating Manchin or Sinema to do fuck all, which he isn't. Sinema can't be moved because she's convinced everything she's doing will give her the bipartisan cred she needs to propel her into the presidency, and Manchin will only be persuaded to do anything if his wealthy donors agree, which they don't because he's basically Republican lite. It's just that Republican lite is the only kind of Democrat that can get elected in highly conservative West Virginia. He's useful only insofar as we get Senate Majority Leader Schumer instead of Senate Majority Leader McConnnell and shouldn't be counted on for anything beyond that. Beyond that, just in general the idea that the president in any way has leverage to force the Senate to do anything is horseshit; the system is designed to give Congress the power to enforce their will on the president, not the other around.
Voting rights certainly are critically important, but the reality is that the Democrats only just barely have a majority solely by virtue of being able to break ties in their favor. Any meaningful legislation would require bringing Republicans on board (which will never happen, because they see politics as a zero-sum game where the other side winning means they lose).