This is a good primer for Soviet-style popular/classical music, while an Amazon search for ‘russian orthodox’ will provide plenty of options down that route.
Gotta go with my Man Main Sergei Prokofiev: Symphonies 1 & 5, Lt. Kije, and Alexander Nevsky are all great places to start (not to mention Peter & the Wolf).
Not in the same league, but I too like Rimsky-Korsakov. This has most everything you’d need, over a nice range (though I’m a particular sucker for “Christmas Eve”).
The lead singer, guitarist & songwriter is Ukrainian, and the accordion & violin players are Russian. They also frequently include russian lyrics. I think they’re qualified for this thread, personally.
But for something more “russian russian”, try DDT.