WASHINGTON — President Joe Biden clinched the Democratic presidential nomination Tuesday, NBC News projects, winning a majority of the necessary delegates and setting up what is expected to be a bitter, closely contested rematch with Donald Trump.The outcome had never been much in doubt. Biden faced token opposition as the party’s biggest names — Govs. Gavin Newsom of California and Gretchen Whitmer of Michigan among them — opted to sit out the race rather than challenge a sitting president who had already beaten Trump once.By clearing the field for Biden, 81, Democrats have…