I think Putin and his lackeys have a problem trying to describe this as an “invasion” mainly because they never really considered Ukraine a separate country, it was supposed to be a vassal Russian state with some local quirks, nothing more. So their invasion of Ukraine isn’t really an invasion on their part, just quelling a rebellion.
So the Ukrainian invasion of Russia cannot be an “invasion” because it’s already Russian in their minds. It’s the rebellion spreading, as deep down they are unable to think of Ukraine as a separate country.
Putin signed a decree allowing persons “who share traditional Russian spiritual and moral values” to obtain a residence permit in Russia without taking into account quotas and language skills.
It is likely aimed at foreigners from Europe and America.