> Nor are they a “exiled Russian media”. They were founded in Latvia.

Founded by Russian journalists in Latvia after one of the founders were fired from a Russian media outlet for work unpopular with the Russian government, initially staffed by former employees of the same Russian media outlet.

So, “exiled Russian media” is (if somewgat awkwardly phrased, “Russian exile media” would I think be more natural) reasonably accurate.