Column/list level validations in SharePoint list will be applied at all stages (item creation/update) to all users irrespective of their permissions.
So, you have to change the validation formula based on other conditions so that validation will be applied only when user is creating a new item in list.
- Do not force validation if Approval Status is "Approved" >> for this you need to change formula to:
- Force validation when Created date column is blank:
- Force validation when Modified date column is blank:
Note: You have to add above formulas to list validation settings as you are referencing other columns (like Approval Status/Created/Modified) in formula. Check this thread for steps to add list validation formula: List validation if then syntax