How do you design an immutable class, and why does immutability matter so much in concurrent systems?

public final class Schedule {                         // 1. no subclass mischief
    private final List<LocalDate> dates;               // 2. private final
    private final Owner owner;

    public Schedule(List<LocalDate> dates, Owner owner) {
        this.dates = List.copyOf(dates);               // 3. defensive copy IN
        this.owner = owner;                            //    (Owner itself immutable)
    }
    public List<LocalDate> dates() { return dates; }   // List.copyOf is already
    public Schedule plus(LocalDate d) {                //    unmodifiable — safe OUT
        var next = new ArrayList<>(dates); next.add(d);
        return new Schedule(next, owner);              // 4. "mutators" return new
    }
}
// Records: record Schedule(List<LocalDate> dates, Owner owner) {
//   Schedule { dates = List.copyOf(dates); }          // compact ctor still must copy!
// }