Get section of input passed to the sanitize_callback

Unfortunately if you look at the source the only thing that happens there is:

add_filter( "sanitize_option_{$option_name}", $sanitize_callback );

There is no opportunity to pass along or retrieve any extra information.

On a larger scale I would say if you need section-specific sanitize then use section-specific callbacks. Even if considerable parts are shared with class based code it should be easy enough to neatly organize.