Ottava begin and continue text cannot be saved as independent style settings
Create an 8va line that encompasses more than one system.
From inspector set the continue text to have brackets: (8va)
Leaving begin text as: 8av
The ottava continuation text is altered accordingly.
Now save the continuation text as a style setting (S button).
At this point, the begin text is updated to match the continue text. Removing brackets from the begin text and pressing S removes them from the continue text.
Unlike cresc. and dim. It looks like continue and begin text can't be set differently as a style setting.