What is the ruling on the appearance of a very thin and small white thread on undergarments, with the possibility of removing it without leaving a trace, and is it obligatory to wash everything that it touches if the madhy (pre-seminal fluid) is discharged continuously?

What you found on your underwear, whose nature you were ignorant of and did not verify its expulsion, is ruled to be pure; because the original state is that things remain as they were. What you do by performing ghusl and changing clothes is an act of over-scrupulousness and waswasa (whispers of Satan/obsessive thoughts). So, disregard what you found and pay no attention to it. You are not required to wash what you touched with your hand, for the original state of your hand is purity until you are certain it has touched impurity. Be lenient with yourself and beware of falling into waswasa.