Is a slight discharge of urine from the urethral opening considered to invalidate ablution, and can one adopt the rulings for urinary incontinence and not be meticulous when feeling urine discharge with the possibility of a slight leak?

What you find at the tip of the male organ might be water from ablution (istinja'), not urine. The male organ is like an udder: if left alone, it dries up, but if milked, it yields.

Shaykh al-Islam stated that urine exits naturally, and when it is emptied, it stops naturally. Every time a person opens his male organ, some may come out. If he leaves it alone, nothing will come out. He might also imagine that something has exited, and this is a form of waswas (whisperings/obsessive thoughts). Furthermore, the urine remaining at the tip of the urethra does not need to be expelled, by the unanimous agreement of scholars, neither with a stone nor a finger. In fact, every time it is expelled, more comes, because it is always seeping.

Therefore, we advise you not to prolong your stay in the restroom beyond what is necessary for relieving yourself, as prolonged stay for this purpose can lead to illness. When you leave the restroom, ignore the waswas and imaginations, for their cure lies in disregarding them. Be careful not to miss your prayer or congregational prayer due to these waswas, which Satan uses to mislead you.