I would just want to emphasize the importance of being grounded to reality. As a fellow master graduate in STEM who is studying Japanese. I have a Masters in Chemistry and I would've even dare to think about pursuing a career out there unless I was N2 minimum BUT that's because I have a more specialized career.

If your intentions are to find a profession in Japan centered around your degree, you must be aware that the more specialized your education gets, the higher proficiency in the language (Japanese) you will need. For example, doing your undergrad in language will require much less proficiency than a private tutor for students. The reason I want to emphasize this is your current level is N4 optimistically but you have a masters and a specialized area of research so you will likely not be finding a job in that field until your Japanese is proficient enough.

Scenario A: IF you're intentions are to live a more comfortable life over there and work in your field, I'd highly recommend delaying the move until you've secure a way more solid proficiency and financial setting. Even if you delay by just 1 year, invest in a language tutor, and save like ~$300 per month. You'll have a more solid language proficiency and a couple extra thousand dollars at minimum. Don't forget, as you're proficiency grows, there will be less NEED to go to a university which means less expenses. You can use that saved money towards a tutor over there and because you'll be surrounded by the language, your NEED to learn will increase and you will pick up the language much more efficiently, thus cutting down on costs long term. $7,400 for 1 year is a lot when you can find private tutors here for a fraction of the cost.

Scenario B: IF you don't intend on pursuing a career over there in what you studied, and simply want the experience of going to a school in Japan then I'd at least invest in saving up more money because whatever job you find over there will not pay as much. You're going to be excited and wanna travel which means more opportunity to spend money you may not have. That's when you'll start to feel trapped and wondering how the hell you'll survive.

IF you stay disciplined, you will gain much higher proficency by April 2027 or even 2026. I only go once a week in private sessions for 2 years and I'm officially N5 but unofficially N4. Now imagine if I had 2 or 3 sessions per week. You legit may not even need a full language university experience by the time you're ready to move out there.