This is because the timesheet is not bound to a project, it is bound to an employee by default. There are currently no modules that change that (as far as I am aware).

Also, if you have sufficient access rights (HR Manager) you can approve all timesheets for all users in the system, not just your own. HR is one of the modules that deserves somewhat more attention in the near future.

Based on my use cases, timesheet validation  should go to the Manager of the employee and not to all managers ... In larger companies it create mess if all managers get all timesheets from all employees.

Project manager may have an additional validation role at the Project tasks levels.

These are 2 different workflows, that may intersect or not depending on the companies;

I agree with Ludo that HR module deserves more attention. It is not far away from benig a great module but clearly lack of simple but key functioanl behaviors;