Should someone who experiences intermittent discharge of wady be treated the same as a person with salasil (incontinence), and is he obligated to check for the emission of anything after every prayer?

If you doubt that something has exited after the prayer, the default assumption is that it has not, and you are not required to investigate in order to ward off waswasah (whispers/obsessive thoughts). If you see a trace after the prayer, it is considered to have exited after it and does not affect the validity of the prayer. However, if you are certain that something exited from you during the prayer or before it, then your ablution is invalidated.

Al-Wadi is a thick, white fluid that exits after urination; it does not necessitate ghusl (ritual bath). Its mere discharge is not considered sils (incontinence) unless it persists most of the time.

If the sils is continuous for most of the time, then perform ablution for each prayer after its time has begun, while using something to prevent its spread. However, if it stops for a period during which you can purify yourself and pray, then it does not take the ruling of sils. If it exits during the prayer, the prayer becomes invalid, and you must wait for it to stop before praying, unless you fear the prayer time will expire.