Neutral powers cannot attack neutral territories. They must first declare war on a player power. Russia is simply not permitted to do what you’re proposing.
That said, once a neutral is attacked (and especially if the standing army is not eliminated), it is no longer neutral and is treated as a FRIENDLY territory (again, not friendly neutral - just plain friendly). They don’t belong to anyone, but the first friendly power that walks in during the noncom move picks them up. However, that same friendly power is free to fly over (as they are not neutral).
They basically behave identical to how the Dutch Territories treat the UK.