Does one who has a wet dream and wakes up to find a dry trace, without knowing if it is semen, urine, or prostatic fluid, and then performs ablution and prays, have to perform ghusl?

If you are unsure about the nature of what you saw, whether it is maniyy (sperm/seminal fluid) or madhiy (pre-seminal fluid), you have the option to consider it maniyy, in which case you must perform ghusl (ritual bath) and repeat the prayers missed before performing ghusl. Alternatively, you may consider it madhiy, in which case your prayers are valid if you had washed off the impurity, performed wudu' (ablution), and prayed in a clean garment. This detailed ruling is the fatwa according to the Shafi'i school. If you considered the discharge to be madhiy and did not wash off the impurity out of ignorance, then, according to the more correct of the two scholarly opinions, you are not required to repeat your prayers.