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

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", "")