I am a US citizen living in an EU country (Poland), and I've been living here for close to a year residing with a National D type visa. I have been offered a remote job at a US institution, but they are asking if I am authorized to work in Poland. Is this relevant to ask since I am not working with a Polish (or EU) based company? In other words, if I live abroad and want to work remotely for a job back home, do I need work authorization for the country I reside in?
You may not work while in Poland unless authorised under Polish law. There is no general exception for work online or work for a foreign organisation.
There is however a fairly long list of cases where a work permit is not required. You might benefit from this, eg if you are in Poland as a university student.
To answer your question directly: Yes, you should be authorized to work in the country where you are residing and your prospective's employer question is perfectly legitimate. There is no universal international agreement regarding remote work and Polish law fully applies even to foreign citizens.
Beyond that, work may be allowed based on some generic provision of Polish law (cf. chx's comment regarding Canada), based on your citizenship or some specific international agreement (that's the case for EU citizens in Poland) or based on your visa or residence permit (spouse visas often implicitely allow the holder to work without asking for a separate permission). Alternatively, it might be necessary to secure explicit permission through a work permit, which might actually be more difficult to obtain without a local contract.
Apart from your immigration status, residing somewhere while working remotely might create other liabilities for you and your employer. For exemple, you might become liable for income tax or have to contribute to the local healthcare and welfare system. This would apply even if you were a Polish citizen who undoubtedly has the right to work without any permit or visa.
You are a non-EU foreigner living in Poland. If you want to work in Poland, you need a work permit. Whether you are working for a company outside Poland doesn’t matter, you are in Poland and working in Poland.
If you are working in Poland already, you better have a work permit. So if the answer about the work authorisation is “no” then you may have been breaking Polish law for ages.