Using conan to package multiple configurations of preexisting binaries

I have a set of third-party binaries that I am trying to put into a conan package. The binaries are in folders for the build configuration: Linux32, Win32, Win64, Win32.

I have been able to produce a conan package for the Win64 configuration using the following conanfile.py:

from conans import ConanFile

class LibNameConan(ConanFile):
    name = "LibName"
    version = "1.1.1"
    settings = "os", "compiler", "build_type", "arch"
    description = "Package for LibName"
    url = "None"
    license = "None"

    def package(self):
        self.copy("*", dst="lib", src="lib")
        self.copy("*.c", dst="include", src="include", keep_path=False)

    def package_info(self):
        self.cpp_info.libs = self.collect_libs()

I run the following commands in powershell:

conan install
mkdir pkg
cd pkg
conan package .. --build_folder=../
cd ..
conan export name/testing
conan package_files libname/1.1.1@name/testing

For the Win64 this works as expected. When I repeat the steps with Win32 binaries I do not get a different hash for the package.

I have tried running:

conan install -s arch=x86

However, this still results in the package having the same hash as the x86_64 configuration.

How is the configuration supposed to be set for generating a package from preexisting binaries?