Just adding to this with my experience in Germany:
The apotheke at the main train station in Hannover wouldn't verify or validate a vaccination outside of Germany. I found one nearby, but in an un-touristy area east of the station, who did though. They gave me two prinouts - one per shot - each containing its own QR code. I scanned those into the Swiss COVID Check app, got the green checkmark, and was able to use that for the rest of the trip.
This was about a month ago.