I am not sure if this is planned or not, but when we have the ability to update Resource Status through SYNCHRO Field, there should be an option (or Automatic) to change the status of the Task from Planned to Started, and also update the date to reflect the first Earliest Status date of all the Resources assigned.
This feature has been released in SYNCHRO 4D Pro 2021.1 (v6.4). Details can be found in the release notes and look for feature Recalculate Task Progress" tool to set task Actuals from Resource Status Dates.
Also have the ability to change Task Status through Field itself.