Oh yes, Putin is always trying to be as scary as possible. Both in an attempt to make Ukraine give up, but also in an attempt to make their allies give up. The truth is Putin lost already in the early days, when Zelenskyj refused an airlift out of Kiev, an stated he needed weapons not a ride.
Putin tries to manipulate and scare to influence politics as you say. But luckily not everyone is falling for it. It's mostly the weak minded like Trump.
But the story about mobilization of up to 500000 troops is not a Putin story, that's a Zelenskyj story and many analysts making that warning.