Is it obligatory to continue with the milking (expressing) after urinating to ensure the exit of residual drops, or is it sufficient to pour water after purification with paper, without concern for subsequent wetness?

There is no need to squeeze the penis after urination ceases. It is sufficient to wash it with water or wipe it with a tissue, then sprinkle some water on it to make it contract and remove any doubt, as Sheikh al-Islam said: "It is recommended for one who has performed istinja’ (cleaning oneself after relieving oneself) to sprinkle water on his private parts. If he then feels wetness, he should say: 'This is from that water.'"

If urine continues to flow after istinja’, wait until it stops, then perform istinja’, make ablution, and pray immediately. As for one who suffers from urinary incontinence that does not stop, he should use a protective pad, perform ablution for each prayer, and pray even if urine flows, as Sheikh al-Islam said.