user input producing incorrect boolean

[buran]

In first snippet it was not working because you were checking that string 'menu_ask' is in the menu. Note, not the variable menus_ask which has value pizza, but literally the string 'menu_ask'

In the second one you introduce different error.
you create new variable new_menu which has 'soup` as part of the string
still you check in menu, which does not have soup
you want to do
menu = menu + ", " + add_item

I see that assignment indeed ask menu to be string keep the list for future

string formatting is not what you think

print('{} in the new menu = {}'.format(men_ask, menu_ask in menu))

or with f-strings

print(f'{menu_ask} in the new menu = {menu_ask in menu}')