What would you call someone who is economically a social Democrat (supports things like Medicare for all, tuition-free college, strong labor unions, tariffs to protect manufacturing), but also supports ethno-nationalism (wants to restrict immigration, favors homogeneous countries)?
Short answer: there seems to be an extant term for this, which is Left-Wing Nationalism.
Left-wing nationalism, leftist nationalism, socialist nationalism, or social nationalism (abbreviation for socialist/social democratic nationalism) describes a form of nationalism based upon social equality (not necessary political equality), popular sovereignty and national self-determination. Left-wing nationalism typically espouses anti-imperialism. It stands in contrast to right-wing nationalism, and often rejects ethno-nationalism to this same end, although some forms of left-wing nationalism have included a platform of racialism, favoring a homogeneous society, a rejection of minorities, and opposition to immigration.
The policy you're describing is a combination of socialism on economic issues and nationalism on social issues. However, here is what is misleading about the question: it sounds like you're fishing for an answer of "this person would be a National Socialist," which is what Nazis called themselves, but what you describe is not Nazism. I doubt it's a coincidence that you combined nationalism and socialism on accident. At any rate, here are the complications in matching-up the term "National Socialist" with what you described...
- Although Nazis defined themselves as national socialists, they weren't economically socialist. The economics of Nazi Germany were purely nationalist. They chose to incorporate "socialist" in their name to co-op the exist socialist movement in Germany. The difference between socialism and nationalism is that socialism shares prosperity with its people, and the state absorbs prosperity for itself under economic nationalism. Many modern conservatives have slung around the term "National Socialist" to incorrectly equate Democratic Socialists with Nazis, when these two things are quite different. So the risk of this term being confusing is quite high.
- The definition of Nazism spans vast number of characteristics beyond simple nationalism. It is essentially a subset of the blanket term Fascism with some distinguishing traits, including racism and antisemitism, that weren't as central to Italian Fascism. Economically, Nazism is nationalist.
- The original question states that this politician is a social democrat on economic issues, but it sounds mostly just socialist. Social Democracy is a kind of Liberal Democracy, and if there was any sort of Liberal Democracy within these policies, I don't think it would be ethnically nationalist. This is because social democracy is concerned with curbing inequality and oppression, which is contrary to closing your borders and turning your back on immigrants.
Social democracy is a political, social and economic ideology that supports economic and social interventions to promote social justice within the framework of a liberal democratic polity and capitalist economy.
Modern social democracy is characterized by a commitment to policies aimed at curbing inequality, oppression of underprivileged groups and poverty, including support for universally accessible public services like care for the elderly, child care, education, health care and workers' compensation.
- If you call something National Socialist, without intending the Nazi connotations, then small-thinking reductionists will treat it as identical to Nazism.
In many ways, the system you describe reminds me of Authoritarian Socialism, which was the government / economic system that we commonly associate with countries that we call "Communist," e.g. Maoist China and Soviet Russia. In reality, they can't be properly Communist, because Communism prescribes a stateless society, and these countries had very strong states. The difference between Authoritarian Socialism and the government you describe is that the government you describe may not be as internally oppressive as Authoritarian Socialism tends to be.