Thank you. I need it, have been involved with covid related problems (over here) for over a year. It has been a year of hell on earth for me, don't know when will it end.. Seriously, I don't wish this for anybody, ever. In Germany - you need vaccine approval from the ministry of health - both federal and state. GP's only involved after you have that, but their involvement is in form of an other letter/paper - your full medical history and recommendation for vaccine (or denial if the particular medical case supports that).
The 3 hours at the vaccination center is mostly checks & balances. Obviously the vaccination itself takes a few minutes.
