How to make existing fields available to be created as instances on other content types etc.?
An 'existing field' in that context is one that already has an instance, it doesn't refer to the existence of the field type. Until an instance is created, it doesn't exist as such.

Your field will be available to add as a new field as usual; if you want it to appear under 'Add existing field' section, you'll need to create an instance of it first.