Nah. Feora is just another moustache twirling villain who's evil plots are constantly foiled. Like that time she lost to Stryker (haha she lost to Stryker) and had to set a church full of people on fire so she could escape.She's young(ish), ambitious, ruthless, powerful and intelligent and even if Kreoss' star keeps on rising, she's still best placed to become the leader of the Protectorate upon Sevvy's eventual death.
Feora may try to take over the Protectorate but we all know Kreoss is going to pimpslap her HARD. She has absolutely no chance against him. Ever. Plus Kreoss has a horsey now, so you know he means serious business.
I dunno if she hates Severius like she hates Kreoss, but she certainly doesnt feel as secure in her position now that Voyle is dead. Voyle was pretty much the only one who saw her as an asset rather than a liability. Although it honestly wouldnt surprise me if Voyle comes back to life "LOLOL WASSUP GUYS IM BACK OH BY THE WAY MENOTH SAYS HI."She and Severius have hated each other for years so no she just hates him but she probably would have been upset if anybody but her was made Hierarch.