How so? Your game is published. It shows up on your creator profile, and you can share the link anywhere. It just doesn't appear in searches. As of this writing, that should take another 12-24 hours.
(Thanks for the help, GarBenjamin.)
Viewing post in Game not appearing in search after publish
The email specifically says "Splody is now published" and then "every new project appears in recently added when first published", with a link to where it's not appearing right now, so that's pretty confusing. Also, as someone who's coming from other stores, I'm getting on itch.io to get a little more exposure to a different audience, so I'd consider the hosting part that is currently live only a small part of "publishing," the other part, much more important to me, is actually being in the store.
Thanks for the detailed response!