That should get you a bit further.
Watch out for the Units deprecations depending on the version of Revit you are working with
from pyrevit import script, revit, DB, HOST_APP
output = script.get_output()
output.close_others()
doc = revit.doc
uiapp = HOST_APP.uiapp.Application
units = doc.GetUnits()
if uiapp.VersionNumber > '2021':
unit_types = doc.GetUnits().GetModifiableSpecs()
# display unit types names
for i in unit_types:
output.print_md(DB.LabelUtils.GetLabelForSpec(i))
else:
unit_types = doc.GetUnits().GetModifiableUnitTypes()
# display unit types names
for i in unit_types:
output.print_md(DB.LabelUtils.GetLabelFor(i))