Why would the russians care to have a cover story? They're in an open hot war with the west.
russia wont openly invade Baltics/NATO, they will send little green men under the cover of some self manufactured crisis. A big forest fire, chemical spill, maybe an aircraft crash or terrorist attack. Then it will be "touch our guys and we Nuke you" like they keep saying in Ukraine, with West trembling to cross magical imaginary red lines.
It's an open war with Ukraine only so far. And many are not aware of the wider geopolitics of it, they don't know their countries are at war with Russia. Open attacks would scare many of those people and make them more hostile towards the Russian side. As it stands many are more neutral and Putin even has a significant number of fans in the West.