Fascism isn't when there's a "private" economy and a "state" economy and they kiss in the closet. I'm sorry but this is just infantile. Fascism is the war footing of the bourgies in a class war. It's a specific thing. All capitalist states on Earth have "an inextricable bond between private capital and the state". They run the state! Capital controls the state in all capitalist nations. That doesn't make it fascism, it makes it capitalism. Fascism is a subset of that which requires anti-communism and violent privatization and destruction of labor. Under Putin's administration Russia has actually done the opposite, re-nationalizing much of what the Yeltsin gang sold off and privatized and improving labor rights from where they were in the 90s 'liberalization' period.

As for LGBT rights, plenty of capitalist nations (non-imperialist ones too) have reactionary social views due to economic collapse and educational collapse. The 90s really did a number on the population of all ex-soviet states, the US spread blackest reaction to all of them but especially Ukraine where it continued its decades long project aerodynamic and worked on taking direct NATO control with Nazi proxies. Consider Palestine, Afghanistan or Iraq. They are not "fascists" because they have reactionary social views. They are socially reactionary, but that's not sufficient for fascism. You are extremely imprecise with your words.