Moving from Osaka to Tokyo as an High schooler

So, I’m an 18yo high school student, I’ve been studying here for some months now and will be living with an host family until about next August.
At my current level I am easily keeping up with high school here, altough i still of course have some troubles with specific Kanjis, and my 校長先生 told me that in case it was possible for me to renovate my visa (which will be ending in november of next year), I could finish high school here and he would be ok with it (there would be about 6 other months to do before graduation, so not that much).

Now, Osaka is an amazing place, I live about 10 minutes from Umeda and so have access to any place in Kansai with little effort, but at the same time i always had my sights on Tokyo, and looking at universities for international students, Waseda and Keio currently look like the best options, so I have even more incentives to want to move to Tokyo.

When it comes to where i’d live, i am lucky enough to be able to afford a flat by myself, especially if also doing part-time or tutoring (I could go for Italian being a native, but i think english tutoring as an Eiken1/C2 is easier both when it comes to teaching, and finding customers), so the main issue would be finding a place to stay, which could become easier if I ended up sharing a place either with other students or with a friend.

So, what’s the point of this thread? Put simply I haven’t got the slightest idea on how to do it (moving), while i think renovating my Visa won’t be hard as long as i can prove I am continuing my studies here, the main issue is of course finding a school itself. Now i’ve done some quick searches online about international schools in Tokyo (since while yes, I can and do study in Japanese, it would still make it way easier for me to handle a different program if it was mainly in English), but I couldn’t find any concrete answer on which schools, if any, do actually give Japanese high school degrees. if it’s not possible to receive japanese High school diplomas from international school, I would love to find out on how do I send applications for Japanese high schools, or if I have to do any specific task for it.

I’m confident it is possible for one to change school at the end of the trimester, since Japanese kids whose parents change job locations already do that, but as a foreigner I don’t really have the knowledge to handle this kind of thing, so if anyone has any experience, maybe having done something similar in the past, or if they’re teachers that know how this kind of thing works, or even if you have any school recommendations, that would help a ton! I’m open to answering questions too.

Oh and an important thing to notice, while I am indeed a foreigner, I wouldn’t be a 留学生, just a 外国人 that is also a 日本高個性, so any handling part of that would have to be the same as if a native Japanese was moving, not as an exchange student.

In any case sorry for the long read and thanks to everyone in advance! I hope i’ll find at least some answers or recommendations since i really want to be able to continue my studies here, but i would love to find an international school to do so.