Does (prostatic fluid/precum/madhiy etc.) require washing the part of the cloth stained? Does it require washing the private part?

In the name of Allah the Compassionate, Merciful. I want to talk about the necessary things that need to be done if I get some prostatic fluid on my clothes. If I'm on the bathroom, I'd inshallah be alright, because I'd easily be able to wash, but not so much if I'm out in public. There are a number of sayings, or hadiths, around 29, that I found at sunnah.com , about this situation. Most of them included some form of washing the private part or washing the clothe. I also care about the opinions of the scholars, especially the four main schools of thought in the Sunni branch of Islam. For example, for washing the clothes, here is one, Sunan Abi Dawud 210 , > Narrated Sahl ibn Hunayf: > >I felt greatly distressed by the frequent flowing of prostatic fluid. For this reason I used to take a bath very often. I asked the apostle of Allah (ﷺ) about this. He replied: Ablution will be sufficient for you because of this. I asked: Messenger of Allah, what should I do if it smears my clothes. He replied: It is sufficient if you take a handful of water and sprinkle it on your clothe when you find it has smeared it. Here is one of those about washing the private part, > Yahya related to me from Malik from Zayd ibn Aslam from his father that Jundub, the mawla of Abdullah ibn Ayyash, said, "I asked Abdullah ibn Umar about prostatic fluid and he said, 'When you find it, wash your genitals and do wudu as for prayer.' " So, are these only recommended or is washing the private part and the stain necessary?