In this work, the low-frequency noise (LFN) characteristics of hafnium-zirconium oxide (HZO) ferroelectric field-effect transistors (FeFETs) with and without high-pressure forming gas annealing (HPA) treatment are investigated. The origin of <inline-formula> <tex-math notation="LaTeX">1/ {f} </tex-math></inline-formula> noise in the FeFET without HPA is changed from carrier number fluctuation to Hooge's mobility fluctuation after wake-up due to the remote phonon scattering from the polarized HZO. Also, Hooge's parameter is increased by the program/erase (P/E) cycling-induced stress. On the contrary, only the correlated mobility fluctuation is increased after the wake-up in the FeFET with HPA. Furthermore, the LFN of the FeFET with HPA shows robustness to P/E cycling-induced stress after the wake-up, showing superb endurance performance.