Hello 
I called the Embassy (Consulate General of Japan in Italy) and they assured me that, as long as my Italy based company agrees, there will be no problem working full remote while living in Japan under a Tourist/Student Visa or any other non-working Visa. I know that the Embassy is a reliable source, but the operator’s voice sounded a little bit shaky so I’m writing to hear some opinions… I also contacted an accountant in Japan, but I’m still waiting for answers. I’m starting to think that it’s impossible to stay in Japan for more than 90 days without being either wealthy, or married to a permanent resident, or one of those people that keeps on going in and out of the state 
Probably it is okay to work for an Italy based company remotely on a Tourist visa, but that won’t give you a status of residence in Japan. That means you won’t be able to get a bank account, phone number, etc, and will have challenges renting anything outside of temporary accommodation. Additionally, if you do this repeatedly, you’ll likely be rejected from entering Japan (I’ve heard that if you try it more than twice a year you’ll be rejected).
A student visa does give you a status of residence. However, you need to be enrolled in an appropriate institution, and it basically means you need to be a student full time. Attendance to school is a condition of the visa, and if you miss too many classes it will be revoked. With this visa, you can apply for permission to work 28 hours per week. You can do those 28 hours for an international company, but it’ll be tough with school on top.
If you’re 30 or under, a working holiday visa is an option. It looks like Italy and Japan just signed an agreement in May 2022. Under this you could continue to work remotely for your Italian company.
Another option might be to use an Employer of Record service such as Deel that operates in Japan. They may be willing to sponsor your working visa on behalf if your employer contracts with them. They also have an option of hiring you as a freelancer, and turning around and billing your Italian company, which even if you use another visa, might make the arrangement an easier sell, as they’ll avoid getting into any legal issues with having a contractor in Japan.
The other option would be to start your own company in Japan, and apply for an investor visa. You’d likely need access to a fair amount of capital to do this (at least ¥5 million, of which you’d spend ¥1-2 million on setting up the company).
Thank you Paul, I asked my accountant about the Employer of Record service, but I think my company would never spent time and money for me on this idea…
I knew about the working holiday but there aren’t many information available yet Also it’s just a one year delay of the problem, if after this experience I want to actually live in Japan, I’ll be at the starting point again.
Also I would like to leave here my accountant’s answer about remote working on a short-term visa and visa runs, maybe it will be helpful for someone:
"1.A short stay visa does not allow you to work. This means that even remote work is not allowed. If immigration find out about this you would be liable to being deported and barred from future entry into Japan.
2.As for doing visa runs (i.e. coming for 90 days and then going to another country and returning for another 90 days). This is a complicated issue. It seems to be generally allowed up until 180 days in one calendar year but after that you may be denied entry. They may also deny you entry before 180days if they are suspicious that you are working in Japan. I couldn’t tell you 100% that this would be fine because the final decision is ultimately down to the immigration officer at the airport."
As far as I’m aware, there is no way for you to work remotely for an Italian company in Japan on any visa. You will need a status of residence that has no restrictions on the kinds of work you can do (eg. permanent residency, citizenship, spousal visa, etc.).
Working on a tourist visa is not allowed. Working full time and/or for a non-Japanese company on a student/working holiday visa is also not allowed. Any work visa you get will need to be sponsored by a Japanese company, and is only valid as long as you’re working for a Japanese company (in the case of a highly-skilled foreign professional visa, the same company that initially sponsored you). An employer of record, as Paul mentioned, would satisfy this requirement.
Unless you are eligible for a status of residence that isn’t tied to employment, you won’t be able to live in Japan and legally work for an Italian company. People do work on tourist visas, but it’s not legal.