does have a Germanic
It's Latin. Servus is 'slave'. It has originaly meant 'at your service'.
The same kind of greeting as in
'czołem' - 'bowing with the forehead', or
'służba!' - 'servitude' 'service'.
Greetings older than that are:
'pomagaj Bóg' - may God aid you
'daj ci Bóg dzień dobry' - may God give a good day
Farewells were:
'z Bogiem' - 'with God'
'do następnego' - 'till then'
'na razie' - 'for now'
'żegnajcie' - 'farewell'
'bywajcie' - 'farewell'