The "Publish" section of the GSuite Marketplace SDK in the Google Cloud Platform is not currently functional for add-ons, as far as I know. The "Update" button is disabled, and it can not be enabled. I don't know if you might be able to click Update once, or something like that, but then it's disabled. But, you don't need to use the "Publish" section of the GSuite Marketplace SDK, in order to publish to the GSuite Marketplace. But, I believe, that there is two separate approvals. One for CWS and one for GSM.
If your listing showed up in the CWS as a Chrome Extension, then you did something wrong. Probably you uploaded a manifest file? That will create problems. I'm not even sure that you can somehow fix it. You might need to scrap everything, make a copy of your script file, and start over again. Whatever you do, DO NOT USE the "Upload" section of the Chrome Web Store developer dashboard. When you "Deploy as add-on" from the Apps Script editor, the Apps Script editor uploads the file automatically.
I've created a video, trying to provide some information. It's not a complete explanation, but might be helpful.