I have read very divergent stories about what really happened, one of which being that Stalin had them bombed to stop Hitler from holding his birthday party there. Surely this can't really be what happened?
I cannot find a source stating that Stalin intentionally bombed the Winter Palace for any reason.
I'm also not finding a source saying that Hitler had specifically planned for a birthday party in Leningrad at all. However, he did have plans for a victory celebration in the Tsar's Palace in Leningrad.
Were the palaces bombed? Definitely, by the Germans. The siege of Leningrad was a long and bloody one, lasting nearly 900 days, and ending in a victory for the city. Inevitably, massive bombings took place, and inevitably, the palaces were likely damaged because of these bombings by the Luftwaffe, not by the Soviet Air Force.