In the book 1984, the country was at war with another country. Then they changed which country they were at war with overnight, modifying history books to pretend they had always been at war with that country. The public just went along with it.

If Putin wants an exit strategy (I’m not sure he does), he can simply declare that all terrorists were defeated and the “special operation” achieved its goal. Then hold a victory parade and have state media say that Russia won. The Russian public would be so glad the war was over that they wouldn’t care.