When changing the date filter to update the project start date, nothing happens. The Start Date for the task remains the same. I'm not sure if I am updating the wrong properties or If I need to include something else.
At the onChange method, you're passing the $event as a parameter, with that, if you check the value variable here setProjectStartDateChange(value : any) you'll see that the correct value is passed inside it as a property, if you change to this everything will work correctly
setProjectStartDateChange(event: any): void {
const date = event.value;
this.gantt.setStartDate(date);
}