Before you attempt to publish an add-on, it's important to understand how add-ons are classified for publication purposes.
Every add-on is in one of two possible publication states: published or unpublished.
Published add-ons have successfully completed the publication process. If published publicly, an add-on appears in the Chrome Web Store or G Suite Marketplace or both, for anyone to find and install. Add-ons can also be published privately, allowing its use for a specific organization or individual only.
Unpublished add-ons are just that—they have not been fully published to the Chrome Web Store or G Suite Marketplace. This does not mean they are incomplete—it is possible to create and use an add-on without publishing it. You can even share unpublished add-ons for others to use.
Published add-on visibility
When configuring your add-on for publication, you must choose to publish it as either a private or public add-on. This is the add-on's visibility.
Private add-ons are only visible to users in the same domain as the add-on publishing account. They can't be installed by outside users. Private add-ons do not require add-on review. Private visibility is sometimes referred to as My Domain visibility.
Public add-ons are visible globally in the G Suite Marketplace. Anyone can see and install them if their domain policies allow it. Public add-ons must go through the add-on review process before they are published. This review process can take a few days to complete, and may require you to make changes to your add-on code.