What should one do if a fluid—believed to be wadī—comes out after urination and does not stop, and is their prayer valid while this fluid continues to discharge?

If the discharge stops, you must wait for it to cease, unless you fear the time for the prayer will expire. If you pray while the discharge is still flowing, the prayer is invalid and must be made up. However, if the discharge is irregular, then the ruling for one afflicted with سلس (incontinence/continuous discharge) applies to you: you perform ablution (wudu') after the time for the prayer begins and pray as much as you wish with that ablution until the time for the prayer ends, while using a cloth to prevent leakage.