For public services, entry level sw engineering with a master's degree would put you at ~52k€ (TVöD E13 I); with 1 yr of experience you would get ~+5k€; with around 3 yrs of experience you would get ~+9k€, surpassing the median salary if you have a master's degree. With a bachelor's degree you'd start at ~46k (TVöD E11 I, though E10 would be possible, too) and would need to wait a bit longer until you surpass the median. Note that German public services generally base your base pay on your qualification (your degree), only then can your experience "shift" the base pay upwards. Also note that starting next year, they will get a 10 % salary increase...

Tl;dr public service employees earn pretty average