Yes, the batteries and rechargeable batteries are included on sale with the Panasonic KX-TG6823. The device comes with the batteries required to operate the handsets.
According to the manufacturer, this model does not have a headphone jack. So the use of a headset is not possible
Source: https://www.panasonic.com/de/consumer/telefon-fax/telefone/schnurlostelefone/kx-tg6823gb.specs.html
Unfortunately, it is not stated on the product page that the product cannot be put into operation like this in Switzerland. I already suspected this when I saw on the package when I unpacked it: "This device is intended for connection to the analogue public telecommunications network in Germany".
In fact, there is only one special plug with which the base station can be connected, "normal" connecting plugs do not work. It is also warned in the product not to use other plugs. It would be nice if this were included in the product description.
What you call a "special plug" will probably be the common telephone plug (TAE) from Germany. https://de.wikipedia.org/wiki/Telekommunikations-Anschluss-Einheit
In Switzerland there is no standard telephone plug. So Digitec would have to add a whole bundle of cables to cover all eventualities. But since there is no legal requirement for such a thing for telephones, of course no seller does this either.
The fact that the instructions for a product warn against using plugs other than those supplied is simply a safeguard on the part of the manufacturer. This is possible with a telephone without any problems.
Why don't you make an enquiry to Digitec customer service so that you can find a suitable connection cable for you? https://helpcenter.digitec.ch/hc/de/requests/new
Unfortunately, with the new IP phone technology... Once the handsets are connected to the router, everything is managed via the router. Date and time are read from the internet network. And phonebook is on the router to configure (if you have access to the router).
Maybe it can still be solved:
-connect the main telephone station to the router via an analogue connection (not wireless).
-and connect the two handsets via radio to the base station (not to the router)
Then you might have a chance (but it's not certain... unfortunately it depends on the router).