Visa-wise, freelancing is challenging. There isn’t any way to self-sponsor a working visa in Japan. Rather, you need to have one of your clients sponsor you, which involves some paperwork on their part. Furthermore, you need to have an ongoing contract with them that pays you a living wage (this is up to immigration to determine, but typically at least ¥250,000 per month). Sponsoring your visa in this manner is only an option if you already have a working visa here, and are just looking to renew it.
Because of this, you’re right that an international company won’t be able to sponsor you. Theoretically though, if you were to set up your own company, you could have your company sponsor your visa, even if you only had one client. Of course, setting up a company is more involved, and its own challenges.