PackageKit(and anything that uses it) fails to work with a proxy.  This makes gnome-software unusable as well as all features that gnome tries to rely on for installing software when its needed (like drivers or codecs).  Manually running dnf works fine for updates or installing software.

For example:
$ pkcon refresh
Command failed: The proxy could not be set: GDBus.Error:org.gtk.GDBus.UnmappedGError.Quark._pk_2dengine_2derror_2dquark.Code3: setting the proxy failed: failed to get the session


Verbose logging reports this:
$ sudo killall packagekitd
$ sudo /usr/libexec/packagekitd --verbose
15:18:35	PackageKit          Verbose debugging enabled (on console 1)
15:18:35	PackageKit          daemon shutdown set to 0 seconds
15:18:35	PackageKit          setting config file watch on /etc/PackageKit/PackageKit.conf
15:18:35	PackageKit          Trying to load : dnf
15:18:35	PackageKit          dlopening '/usr/lib64/packagekit-backend/libpk_backend_dnf.so'
15:18:35	PackageKit-DNF      Using Dnf 0.8.0
15:18:35	PackageKit-DNF      Using librepo 1.7.20
15:18:35	PackageKit          trying to open database '/var/lib/PackageKit/transactions.db'
15:18:35	PackageKit          job count is now at 213
15:18:35	PackageKit          PkEngine: acquired name: org.freedesktop.PackageKit
15:18:58	PackageKit          SetProxy method called: http://10.0.0.1:8000/, ftp://10.0.0.1:2100
15:18:58	PackageKit          failed to get session, errno -6
15:18:58	PackageKit          failed to get the session for :1.169
15:18:58	PackageKit          failed to get session, errno -6


The following environment variables are set:
ftp_proxy="ftp://10.0.0.1:2100"
http_proxy="http://10.0.0.1:8000/"
https_proxy="http://10.0.0.1:8000/"
no_proxy="localhost,127.0.0.0/8,::1,172.29.131.1,10.0.0.0/24"
rsync_proxy="10.0.0.1:8000"


See redhat bug https://bugzilla.redhat.com/show_bug.cgi?id=1348843