Problems adding custom field formatter
You are not supposed to see the settings form in Manage Fields > edit (a specific field) > Field settings as you expect. Formatters are used for managing the display of fields (theming). So, go to 'Manage Display' tab (for your Content Type) and choose the view mode for which you want to manage the button visibility (default, full content, teaser, e.t.c). Find the field(s) you wish this functionality to be applied, and then select as 'Format' option, the label of the formatter you just created, which in this case is 'Copy to Clipboard'. Then if you click on the cogwheel icon on the right, you will see your settings form. Note that this setting will be applicable to all instances of this CT for the specified field for the specified view mode. 

If you want other fields of the same CT as well, you need to repeat the process for the other fields as well. If you want this functionality for additional displays of this CT (e.g. teaser view), then you need to repeat the process. And of course, repeat the process for all CTs/view modes/fields as well. This is because Drupal offers much flexibility and variety in displaying content. If you want such a functionality to be applied globally (e.g. for all CTs, for all text fields) then perhaps you should consider another strategy; a new theming function or override of an existing one for example.