Thinking about your stories another idea struck me. Ukraine can't take back their territory by force, at least not in the near future. The most likely way for Ukraine to win is for the Kremlin to lose control of inflation (rubble). A way to do that is to rattle those in Moscow / St Petersburg--especially those in the FSB and all other government agencies.

When Ukraine entered Kursk the closest police forces of any size are in Moscow. They need to be sent down to police Ukraine out--Ukraine, to our knowledge, does not have the force to repel them. So Putin is in a huge dilemma.

Send down police units to push Ukraine out, or at least prevent them from going further (risking a huge social backlash in Moscow as their families experience war first hand) or let Ukraine have the territory for now until army units can get there.

So that's my theory of the moment, but inspired by you. Putin offering people who had to leave the area $115, well, if Ukraine does have the plan I'm thinking about, Putin has taken it hook, line and sinker.

Finally contrast this with Russia's move on Kyiv. Every police officer and accountant went to defend to the point they had to be turned away. No one in the Russian media is suggesting anyone volunteer ;)