Japan actually has a lot of foreign nurses (largely from the Philippines as with many countries). It is a higher barrier to entry due to needing to know not only regular and business japanese but also medical jargon and be able to pass tests in japanese on it.
I imagine immigration in that sector will grow (it’s not mutually exclusive to robotics), particularly as the older generations die out.
I’ll take minor issue here. If you have a 4-year degree and a company sponsor (sometimes equivilent work experience, but that requires documentation and expenses a company won’t typically want to pay) in a white-collar job, getting here is pretty easy. Even somewhat easier for English teachers. Max visa is 5 years, though they can be renewed. After 5 years, one can apply for citizenship (though must renounce others). Permanent residency is available from 1 (highly-skilled professional), 3 (points system on any 3-year visa with a couple asterisks; marriage), or 10 (not enough points in system, 10 years of working in Japan , and on 3-year visa), and more I don’t know about