Having a half board in Europe, especially in urban areas is rare but it is very normal in Japan when you stay at ryokan type inn. On the other hand, full board is hardly offered in Japan and hotel type accommodation mostly do not offer half board if it the hotel is not located in resort area or hot spring.
The price system is complicated for ryokan type inn than hotels. The price is usually per person, not per room. Then, mostly is a price including half board. Therefore there is no supplement for half board as like in Europe. Ryokan also offers room without any meal(even no breakfast) and room with breakfast(but it is rare case).
Also you have to watch out when booking room with half board. Usually the dinner time will be fixed. Which means you can not have the dinner when ever you want. Then, it is not like the seat reservation of a dining hall, the time will be determined by hotel. For example, the dinner time is 17:30 or 19:30 and you can choose the available slot. Which means no one is coming at 18:00 or 19:00. Then, if you miss the 19:00 slot, dinner will not be provided.