Is it obligatory to repeat the Asr prayer if a small amount of wetness is found around the urethral opening after the prayer, while maintaining wudu, and what is the ruling on "salat al-dhakar" (squeezing or stroking the penis) with a barrier before prayer to ensure purity, given the prevalence of obsessive thoughts (waswas)?

As long as the worshipper did not feel anything during the Asr prayer, the wetness he found after the prayer does not necessitate repeating the prayer; because the hadath (ritual impurity) is attributed to the nearest time.

What he does to ensure there is no wetness is considered an excessive scrupulousness (tanattu') and leads to an aggravation of waswasa (obsessive whispering/doubts). A light squeeze after istijmar (cleansing with stones/tissue) is sufficient. Then, he must refrain from searching for impurity and turn away from waswasa, for indulging in it only worsens it.