Absolutely not - Russian women had less choice following the collapse as the country's economy declined.

The paper I cited does not claim that USSR had managed to transform an otherwise very prejudice society into an equal egalitarian one. Instead, soviets focused on full employment AND full Labor participation as part of ideology, leaving less room for contradictions such as gender discrimination on employment or education itself. Salary and promotion discrimination remained as there ideology provided less cover. Following the collapse, Russian society reverted to its old prejudice self. Lookup домострой if you don't believe me.

Another less from USSR for gender/family stays equality is that childcare access makes a huge difference. In USSR, parents were guaranteed state funded care from the point maternity leave ended to college. On paper that still exists, but in practice it's a shadow of what it used to be.

The role of women in Russian society is very complex, but its not accurate to say that Russian women have more choices post-USSR. The best way to understand the situation is Soviet idealism against the reality of longstanding Russian patriarchy. The Soviets were at the forefront of encouraging women to enter the workforce, making abortion legal in 1920, making divorces easier, providing child care, etc. Those policies suffered fits and starts (Stalin rolled back abortion from 1936-1955) but were still in many ways far ahead of Western Europe. Post-USSR the idealistic stuff died out and there was a strong reversion to patriarchy (not to mention per-capita GDP dropped by half and only returned to peak Soviet levels in 2008).