Wouldn’t the Biden administration want to have the filibuster fight as early as possible so that Democrats can be more aggressive with their legislative priorities?

I think they do not want to force this fight early. What’s being discussed is doing a big legislative package through reconciliation, which is a mechanism for budgetary issues that is not subject to the filibuster that can fast-track legislation to the Senate floor. The rules of reconciliation are so restrictive that it could be used to pass a big COVID aid package, but it doesn’t apply to things like civil rights legislation.

Even if the Biden administration is able to get a lot done through reconciliation, the Biden administration will still face the reality that passing civil rights and democracy reforms will require ending the filibuster. I don’t see Republicans ever giving Democrats 10 votes for automatic voter registration or D.C. statehood, and I think sooner or later that will force that debate to a head.