I looked at the settings again and noticed the tracker blocking. I turned it off and target.com started to work. I logged in and then reactivated tracker blocking and it seems like it's still working. I don't understand the intricacies enough to speculate beyond thinking the website is refusing to respond when some data is blocked. Regardless, this detail might be useful for someone else.
@leocg I've seen screenshots (from the threads about the button to change the speed dial wallpaper) which have a search field. Might only be in phone layout though.