...at least the idea that they were there to fight Ukraine.

having said that reports on the Kursk expedition suggests it has involved a substantual number of foreign "mercenaries"...and the rumours have it, was also a Brit planned operation.
So Putin's angle: if a tease or otherwise, seems to have been "Good for the goose then good for the Gander."

-Not something the hubristic West really accepts under that "Rules Based Order".