Democrats very likely win both Georgia Senate seats, resulting in a 50-50 Democratic-Republican balance in the U.S. Senate, with Vice President Harris casting the tie-breaking vote, making Chuck Schumer the very likely new Senate Majority Leader.
This means Schumer gets to decide what legislation comes to the floor of the Senate (just as Mitch McConnell has for the past several congressional cycles) BUT the Senate filibuster remains, meaning that McConnell (or any other Senator) may require 60 votes (not 50) for anything to be voted on. So Republicans can still stop anything they want, legislatively.
Senate Democrats could, in theory, eliminate the legislative filibuster if they get 50 votes to do so (with Harris’s tie-breaking vote), but there are several Senate Democrats who have previously said that they oppose abolishing the filibuster. So this probably won’t happen, although those Senators might change their minds in the future.
The way that Senate Dems might try to get legislation passed is through the “reconciliation” process that, by law, is not subject to filibuster rules and thus requiring only 50 votes + Harris’s VP tie-breaking vote. This can be used for anything related to the budget, taxation, spending, etc., and in recent years has been used expansively (example: it’s how the Affordable Care Act was ultimately passed through the Senate).
As far as the federal judiciary goes, Democrats eliminated the filibuster on lower-level judicial nominees during Obama’s presidency and Republicans eliminated the filibuster on Supreme Court nominees during Trump’s presidency. So as long as all 50 Democrats are united in support of a judicial nominee for Supreme Court (or any other judicial nominee) OR can get a combination of 50 Democratic and Republican votes, they can pass whatever Court nominees they like.
It’s also important to note that a president’s political party almost always loses seats in both the House and the Senate in midterm elections. Given that reality, the most likely outcome is that Republicans win both the House and the Senate in the 2022 midterms, stopping any of Biden’s legislative agenda and judicial appointments. Thus, Biden has a realistic window of about 12-18 months to pass any of his legislative agenda or make any judicial appointments.