but that was because she met Shirou, she actually wanted to kill herself before meeting him, after that he was her glimmer of hope.
And Shinji wasn't Gilgamesh's master, it was the other way around

If it wasn't Shirou, Sakura would have likely broke down, eventually giving birth to some Matou bastard. If Rin was able to save Shinji in UBW Sakura visits him in hospital and he shows dramatic mental changes, according to the text in0game he started treating Sakura gently and kindly. Events from Heavens Feel were likely the worst case scenario where in her unstable mind shape Sakura starts to "fix" her life, be mindful she even kills Zoken so damn easily I was in awe.