In terms of vocabulary, the Ukrainian language is the closest to Belarusian (16% of difference), and the Russian language to Bulgarian (27% of difference). After Belarusian, Ukrainian is also closer to Slovak, Polish, and Czech than to Russian – 38% of Ukrainian vocabulary is different from Russian which is a similar level of similarity/difference as between English and German (40%), for example.
More Ukrainians understand Russian than Russians understand Ukrainian, basically because, as you say, of the political influence of Russia not because of a shared sense of community.
The basic point is that whilst they share cultural and political heritage they aren't the same by any means (and there are examples of a lot closer cultural independent nations) and to dismiss these differences and a significant proportion of 21st Century Ukrainians desire not to be a client state of Russia as purely down to US meddling is vey wrong (although that isn't to say the US and the EU and NATO haven't meddled and haven't been ham-fisted about it).
I worked in Ukraine, Georgia, Kazakhstan in the '00s and the distaste for Russia at a community level was strong in all 3 countries back then, especially in Georgia and Ukraine. It is the 'puppet' elites in those countries which maintained links to what are seen as former colonisers rather than partners. Significant parts of these populations want to get away from Russia, especially Putin and his Empire building Greater Russia complex.
(The relevance to the price of Borscht was questioning, as with all these things, what part of history remains relevant to the argument - how far back do you allow to go? Russia was part of the Kyvian Kingdom before Ukraine was part of the Russian empire)