Joe Biden won his primary by campaigning as a moderate, and he proved this by specifically rejecting notions such as packing the court. In July 2019, Biden said (correctly) “We’ll live to rue that day” if the court is expanded. In the end, Republican voters will demand that Republican lawmakers get on with the task they were elected to do. Filling a vacancy is normal. Packing the court is abnormal. Republicans are promising to do what must ultimately be done. Democrats are campaigning on something that will blow up the legitimacy of the court.
All of this helps Trump because it puts a more radicalized Democratic Party in the spotlight and pushes Joe Biden and Donald Trump off the stage.
Further, if Trump picks Amy Coney Barrett, the Democrats on the Judiciary Committee and in the media will be sorely tempted to make her Catholic faith and her seven children (two adopted) into an enormous controversy. This is a very bad move when Joe Biden is trying to win states such as Pennsylvania, Michigan, and Wisconsin that have lots of Catholic swing voters.
Ultimately, the vacancy also helps Trump because the Republican Party is never more unified than during a Supreme Court confirmation battle.