Hi Jon,
Apps are always visible in production on every plan. Environments have no impact on app visibility. If you don't enable other environments, your apps will only use production data. If you choose to enable another environment in addition to production, which is always available by default, it only means that you could use the same app with different resource data.
Apps are immediately "published," unless you choose to implement release management. If you use release management you could choose which version is published. In either case, if an app has been created, it is visible to all users that have access to it.
I'm not sure what you mean by depublish an app. You could delete it if you no longer need it, or you could upgrade to the Business plan and control who is able to see it. As soon as you start creating an app on the canvas, it means you have the edit version of the app and the preview/end user version of the app. You don't actively publish or depublish it.
On the Team plan level, all users can see & edit all apps. If you upgrade to Business, you could see a view like this and decide which permission groups can see or edit which apps & resources.
To summarize, on your plan level, if you create an app, it's visible to any user in your org. They can edit it or view it.
The only caveat would be if you share an app publicly. If you are on the Business plan or higher, you can choose to share your apps publicly to anyone with the link. We don't have a dashboard where you can see how many apps have this setting enabled, but you could click Share->Public on each one & enable or disable the setting. Since public apps have no authentication and can be accessed by anyone, they tend to have limited use cases.
Hope this helps, but please let me know!