It is no secret that any language could be weaponized and used as a political tool. That's how propaganda works. However, some Russian linguistic intricacies cannot be fully translated into English with the meaning preserved.
Both "россиянин" and "русский" are translated into English as "Russian." However, the two are not the same. "россиянин" is someone who is from Russia or holds Russian citizenship. However, such a person is not necessarily "русский.”
"русский" is anyone of Russian ethnicity. Such a person could be, say, from Ukraine. Such a person is most likely going to be a Russian speaker too. Things get more interesting when the two adjectives are applied to inanimate objects.
"Российский" is something coming from Russia or made by Russia. "Русский" is something made by ethnic Russians from Russia. That's why the Russian Warship meme is so important. The crew of Moskva referred to themselves as "русский военный корабль." It was not just a warship.
It was a Russian warship made by ethnic Russians. This lines up with the ethnocentric policy that was promoted by the Russian government over the past decades. Russia is a multiethnic state but everyone is required to learn Russian. Kamil Galeev has a great thread on minorities in Russia:
https://twitter.com/kamilkazani/status/1506479259866394625?s=20&t=XRMcUZcYmQYpdAwcUEAm9w
That's why for a Russian speaker it is always surprising to hear a Russian citizen be called "русский," i.e. not just Russian but also an ethnic Russian. It is not always the case. Every fifth citizen of Russia is not an ethnic Russian.
That's is why a slogan that is frequently chanted by some attendees of political rallies (not protests) in Russia "Россия для русских" that translates as "Russia for Russians" might seem harmless to some Western observers.
However, such a slogan has an extreme far-right meaning: "Russia for ethnic Russians." By the way, Aleksei Navalny was spotted at such rallies back in 2011. Maybe he has changed, maybe not. The black/yellow/white is an old Russian Imperial flag used by the Russian far right groups.
So to wrap up on Russian vs. Russian. The delineation between "русский" and "россиянин" is crucial and frequently lost in translations. Russia's ethnocentric policymakers probably love that the two are the same in English. The two are not the same due to Russia's imperial past.
And now the those in power in Russia are trying the blur the line between "русский" and "россиянин." "русский," an ethnic Russian, could be someone born and living abroad, specifically in one of the neighboring countries.
When the lines are blurred, the Kremlin can claim that an ethnic Russian born and living abroad needs to be "protected" by Russia on the same level as a citizen of the Russian Federation. Such rhetoric has been used by the Russian authorities to motivate their imperial ambitions.
Whoa, aren't those obviously not the same? Well, they are the same, according to the current Russian propaganda. Since 2014 the Russian state and affiliated media have been working hard on blurring the line between the two.