The Paragraph Style command can easily be assigned to the toolbar.
Is it possible as well to assign a Character Style command to the toolbar? It would be useful to see at a glance which character style is applied when the cursor is in the text.
There is unfortunately no drop-down menu for character styles.
But you can list the character styles in the style side pane. If it is not already visible, open it with Styles>Manage Styles or F11 (except under MacOS where F11 is intercepted by the OS). The style pane initially shows paragraph styles. For character styles, click on the second icon from left in the pane toolbar.