When auto_type is set to true, how can you get all of the modified parent tasks

The tasks with the project type ignore the date parameters as they obtain them from their children. So, technically, they are not updated.
When you load the data from the database, the project tasks will jump to the correct position depending on their children’s dates, regardless of what dates are saved in the database.

However, if you still need to know that the dates of the project tasks are changed, you need to manually implement a custom solution by using Gantt API and Javascript.
The following examples can help you to start: