YEREVAN, Armenia — When tens of thousands of Russians fled the country this spring following the Kremlin’s invasion of Ukraine, many chose to resettle in Armenia and Georgia. But for LGBT Russians, their new homes in the conservative South Caucasus — where there are few protections against homophobic violence — may mean facing even greater risks than in the hostile environment they left behind. Watching her friends in Russia being arrested for their anti-war activism, body-positive blogger and LGBT advocate Ollie decided to move to the Armenian capital to work with a project helping LGBT people affected by Russia’s invasion of Ukraine.