My knowledge about list operations is from scripting languages. So in Java I stopped on something strange in case of finding cookie with particular name.
Lis
Your current code returns a Stream, so you need an extra step to return a string:
Optional auth = cookies.stream()
.filter(c -> c.getName().equals("auth"))
.map(Cookie::getValue)
.findAny();
Note that it returns an Optional because there may be no Cookie that matches "auth". If you want to use a default if "auth" is not found you can use:
String auth = cookies.stream()
.filter(c -> c.getName().equals("auth"))
.map(Cookie::getValue)
.findAny().orElse("");