I am a host here in Osaka.... and I too am finding it hard to lock down the exact details regarding the collection of copies of passports. All lodgings in Japan regardless of Airbnb, hotels, etc. are requested by the Ministry of Health and Welfare to collect this data.
https://www.mhlw.go.jp/english/topics/lodging/index.html
There has been a lengthy debate on this topic, even here in Japan. If you really are concerned, please read the following link and come to your own conclusion as to what you should do.
https://www.debito.org/?p=13852
My basic protocol is to request all the information from the guest, including a copy of passport. The only reason is that I do not personally check in my guests so I cannot 100% confirm that it is them. However, if a guest refuses, I respect their privacy. I still require their names, e-mail address, number of guests, address, nationality, and passport number.
Easiest way to avoid giving your passport in Japan to a hotel... Just tell them that you live here. Give them an address in Japan. You could for example give them the address of the last hotel you stayed at, and... then they are not required to ask to copy your passport if you are living in Japan. Well... you are, right? For a week or two. 🙂