The 2022 Oscar nominations didn’t go according to script for some of Hollywood’s top stars — including Lady Gaga. The Manhattan-born actress received nominations at the Golden Globes and Screen Actors Guild Awards for her portrayal of socialite-turned-convict Patrizia Reggiani in “House of Gucci,” but was among the most surprising omissions when the Academy Award finalists were unveiled Tuesday. Gaga, 35, was left out of a best actress category where three nominees also played real-life figures: Kristen Stewart for the Princess Diana movie “Spencer”; Jessica Chastain for the televangelist biop…