Does a white, pus-like fluid that exits without ejaculation during sleep, accompanied by a fleeting desire, necessitate ghusl, given that the characteristics of this fluid, its color, and its odor have changed from typical semen due to hormonal imbalance and diabetes?

What is discharged during sleep with lust is mani (seminal fluid), which necessitates ghusl (ritual bath), even if some of its characteristics have changed, and it does not cease to be mani. If you are certain it is mani, ghusl is obligatory. If you are certain it is madhi (pre-seminal fluid), purification and wudu' (ablution) are obligatory. If you are in doubt between the two, you have the choice to assign to it the ruling of whichever you wish.