That button is for asynchronous deployment of a successful build to an existing deployment environment. Octopus deploy is not supported as an environment deployment but this could be achieved with a deployment project.
On click button DEPLOY I want only to deliver one of previously created build to Octopus from chosen branch where I clicked this button (DEPLOY) and in next step manually deploy it by using Octopus to chosen by myself environment. Can I do that? I would like to save time on creating build every time and manually select an environment in Octopus but also have the option not to choose and just to store it in Octopus. On this moment something like upper problem is resolved by using NEW BUILD/REBUILD COMMIT buttons, but it's create a new build and waste our team time.
As far as adding octopus deployment environment, as i mentioned above, it is not supported. This is largely because Octopus itself allows for asynchronous deployments of packages once your artifact is uploaded there .