・ It is not a work visa and provided only for learning Japanese culture.
This resident status/visa is not provided for you to work. Please understand that the main purpose is to learn Japanese culture through unpaid work.
・You will not be paid
Since it is not a work visa, you cannot be paid. If you are found receiving salary for your labor or services, you will face the charge of unauthorized employment.
You need to find a restaurant that accepts you on your own
If you tell that you are looking for a restaurant to work because you want to learn Japanese cuisine, many people will be supportive and help you with the search. Yet, since Japanese restaurants do not have an apprentice system, such as Stagiaire in France, there are not many Japanese restaurants that are accepting foreigners.
For how to find an internship, please see this article.
・You need to cover your living expenses.
Some restaurants may let you use a dorm room shared with other staff members, but basically you need to pay your living expenses. As you are not employed as a worker, you cannot be covered by Workers’ Accident Compensation Insurance either. In case you get injured during the stay, I recommend that you join a health insurance plan beforehand.