The legitimacy of the court is being destroyed by the Republicans, who are using deceitfulness, hypocrisy, and naked power grabbing to install a Supreme Court that is far more conservative than the American public. I have read some analysis that suggests this court, with Judge Barrett on board, will be more conservative (as in, more hostile to civil rights and more friendly to business interests) than any court since the 1930s when the court was busy invalidating every New Deal program that came before it. Any court that seeks to turn the clock back almost a century will be seen as an enemy of the people by most of the population. If adding to the court is the only way to restore some balance, that would be (in my opinion) less damaging than the current direction.
The question the Republicans are demanding that Biden answer is similar to the old "when did you stop beating your wife" canard. It is designed to have no correct answer, and to take attention away from the way Republicans are stacking the court with extremist Federalist Society alumni. Republicans have literally no platform (at least, that they are willing to disclose to the public) other than King Trump, so they have abdicated any right to demand any answers on policy matters from the Democrats.