Welcome to the forum.
It's not unusual for tyres to get a bit shiny, particularly in winter when
temperatures are low and you aren't using the full width of the tyre.
Take them for a spin on a warm dry day and they should scrub in again.
It looks like you have plenty of tread left. The minimum limit here is 1mm and most
tyres have wear indicators at 1mm. I believe there is a more stringent limit in Germany,
possibly 1.6mm.