Question

how producer surplus is made in a long run competitive market even if the producer is not making any profit ?

Answer 1

Producer surplus is an economic measure of the difference between the amount a producer of a good receives and the minimum amount the producer is willing to accept for the good.
So, even the producer faces losses, he has producer surplus, because the market price is above the minimal possible price for this producer.
Reference:
https://www.investopedia.com/terms/p/producer_surplus.asp#ixzz51i1Yyd2C