I have not seen a single German telepsychiatry service, […]
Oh yes there are.
Traditionally done by telephone, a growing number of physicians are providing their services by video conference, too.
In Germany, all practicing doctors have to be in network, the Kassenärztliche Vereinigung.
There are 17 regional networks (North Rhine-Westphalia has two).
Their websites feature (a link to) a physician search form.
For example for the state of Lower Saxony, at physician information Lower Saxony you will select
- Fachgebiet (specialized in) → Psychotherapie (psychotherapy, and possibly others)
- Besonderheiten (features) → Videosprechstunde (video consultation)
- (and probably also) Fremdsprachen (foreign languages) → Englisch (English)
To find your state’s search form, look at the Federal Physician Association’s site.
The search form’s texts vary widely, some apparently do not even provide a facility to search for Videosprechstunde.
Is it possible to receive telepsychiatry from a different EU country?
You have to appear in person once every quarter year at the doctor’s office and get your health insurance card (the EHIC) read for billing purposes.