When I create a new style in a document (Writer or Calc), it is only available in this particular document. How can I copy that style to the default styles available to all documents?
You can import styles from documents or templates. F11, click top right icon > Load Styles and follow the menu.
You also can create a file with all styles you want to have in this file and save it as a template. If you like you can make this your default template.
More details depend on your needs.
Ask if you need more help but explain what you did and what worked out and what not.
F11 toggles the styles pane, but there is no “Load Styles” icon. The top right icon is “Update Style”. Please clarify.