If you're wondering why your app hasn't appeared in the marketplace, this might be the reason:
To let any user find and install your add-on, publish it publicly. When you publish your add-on publicly, the Google team reviews your add-on before it’s published live on Google Workspace Marketplace.
On the topic of how to actually test your app.
Go to Deploy > Test Deployments
Click on the Select Type dropdown menu and select Google Workspace Add-on
Configure your deployment to use the latest code
Press Install > Done
Make sure that your onOpen function isn't throwing any errors that could prevent the script from actually launching.
And as always make sure you're following all the steps from the official docs.
If you need any help testing your AppScript feel free to reach out! I've built a handful of projects with AppScript in the past.