Try setting "Default" property of text control to:
If(PMApprovalDropDown.Selected.Value = "Approved", "PM Approved", PMOApprovalDropDown.Selected.Value = "Approved", "PMO Approved", ProjectSponsorApprovalDropDown.Selected.Value = "Approved", "Sponsor Approved", "")
In place of PMApprovalDropDown, PMOApprovalDropDown and ProjectSponsorApprovalDropDown, use correct names of respective dropdown controls.
Documentation: If and Switch functions in Power Apps
Update from comments:
Add conditions in order from higher stage to lower stage like:
If(ProjectSponsorApprovalDropDown.Selected.Value = "Approved", "Sponsor Approved", PMOApprovalDropDown.Selected.Value = "Approved", "PMO Approved", PMApprovalDropDown.Selected.Value = "Approved", "PM Approved", "")