After installing cockpit-packagekit the Software Updates tab did not appear.
After doing a little digging it appears to be caused by an incorrect path listed in the manifest for the plugin.

In /usr/share/cockpit/packagekit/manifest.json it has the following conditions:

>    "conditions": [
>        {"path-exists": "/lib/systemd/system/packagekit.service"},
>        {"path-not-exists": "/sysroot/ostree"}
>    ],

The path /lib/systemd/system/packagekit.service does not exist with packagekit installed on the system. Instead it is located at /usr/lib/systemd/system/packagekit.service. If I change that line to the corrected path the Software Update tab then appears and seems to function just fine.