Shipping Cost not added to product price

i have allowed my customers to chose the shipping method from the front end.

i tested all the 4 shipping calculation and it is always the same problem

the Problem is after the customers chose there shipping they want.

it gets saved but it is never added to the Product price!!!

also some products are imported whit the shipping name of aliexpress something.

knowing that i changed all Original shipping company name to new replacement
example :

https://catstyl.com/shop/detachable-pet-massage-comb/