Approve a draft payroll, transitioning it from draft to pending for processing. This is the final step of the payroll process.

Flow: POST /payrolls (create draft) → review preview → POST /payrolls/:id/approve.

On approval, the server:

• Submits the payroll for processing
• Assigns paper check numbers for manual-payment employees
• Activates pending pay schedules
• Creates PTO accruals for hourly policies
• Sends confirmation emails and push notifications to admins and accountants
• Creates an audit log entry

Only available for payrolls in draft status. Requires the payroll plan or higher.