What is the ruling on the persistence of purity for the 'Asr prayer if I felt drops of urine exit after the Dhuhr prayer, but found nothing upon inspection, knowing that I suffer from obsessive-compulsive disorder (waswasah)?

The cure for obsessive thoughts is to ignore them and pay them no mind. So, no matter how much you doubt that urine has exited, do not pay attention to this doubt. Uphold the original state, which is the continuity of purity. Pray with this ablution as much as you wish, as long as you have not invalidated it with certainty. Do not rule your purity invalidated unless you achieve absolute certainty, upon which you could swear, that something has indeed exited from you.