"Glory to Russia" ("Слава России") is the name of a national series of patriotic children's contests supported by the President's Fund for Cultural Initiatives: https://www.deti-rossia.ru/. It obviously does not compare to "Heil Hitler".

"Eternal glory to heroes of the Great Patriotic War" ("Вечная слава героям ВОВ") is a common refrain in Russian remembrance of WWII. You will see it on signs and on TV around memorial holidays. It obviously does not compare to "sieg heil".

Russia also had a nationalist movement that collaborated at times with the Nazis, the Russian Liberation Army. And Russian nationalists have attempted to rehabilitate their leader, General Vlasov, since the fall of the USSR, much as Ukrainian nationalists have Stepan Bandera.