How to get hook_form_FORM_ID_alter field value in hook_ENTITY_TYPE_presave
The form field you've added is not a node field.

If you want the field to be accessible in the node, then add it to the content type. In this case you don't need a form alter hook, because the entity fields are added to the form automatically. You can create multiple form modes with and without the field and select them dynamically, for example with Form mode manager.

If you don't want the field to be stored in the node, but want to do something else with the user input, then add a custom submit handler in the form alter hook to process the field value.