Aneta,
Your S84/98 bayonet was probably made around 1940. Look on the back spine of the blade and see if there is a two digit date.
While the grease (plus) is covering up part of the blade - I�m thinking that it might be a later example. Such as a later edition of a mid-war (1943/1944) commercial 98K bayonet by WKC with red bakelite grips. In which case it will not have Waffenamts or a serial number.
As far as being a legitimate WW II German combat bayonet the answer is a yes. FP
How right you are thanks.