> what on earth could they be continuously doing for four years?

It’s not continuous. Court time in particular is a scarce resource. Many people are involved in complex litigation, and for almost all of those people it is not their only project / job.

> My guess is that it's like a poorly run software project: mostly empty, where Person X is blocked waiting on the output of Person Y for weeks, and so on.

Correct but the off times aren’t empty; the lawyers and staff simply pick up one of the other hundreds of tasks in front of them while they wait.