(Not suggesting that that’s the case here; just that you shouldn’t forget how e.g. the US CIA engineers coups in other countries, when thinking about how other large states work.)
Someone in your way? Start a rumor that they do X and then attack them for not stepping down from power. Want to check if people agree or disagree with something? Start a rumor on Friday, monitor for responses, fight in rumors during the week-end and next week, if the rumors align, maybe start that something.
I don't see how rumors are never propaganda.
Yes there are rumours, are they propaganda? I don’t think so in this case - young male Russians are being questioned at the border, flights are being stopped, and the idea has been floated of forced conscription of anti-war protesters. Even mentioning the word war is a crime. Russia is very close to martial law already and I’m not surprised there is speculation about it.
Also, quite frankly no one in the west cares much if Putin imposes martial law, it’s already a pariah state and a dictatorship. As propaganda this rumour would be pretty useless.
No you haven't discovered a vast EU-wide conspiracy or someone 'saying the quiet part out loud'. Nobody knows what is going on and naturally there is lots of speculation to fill the void.