'I can't seem to find it. The "stats" screen for the foreign races seems to be identical whether I've got them on Medium or High level of espionage. Also, after I get "high" can i safely turn off espionage spending for that race and still retain the information?'
There is some extra information in the category stats section (the part that lists 'Best system'and 'Most powerful ship'), IIRC. Other than that, I'm not sure. I'd have to look closer to tell.
'From my preliminary investigation, after you achieve "High" spy level, you can safely turn off all espionage spending for that race. Of course I'm not 100% sure. I'd prefer if one of those brilliant developers stopped by and confirmed.'
Several events change based on your total espionage spendings, you get a bit more of those information pop-ups when you're still actively spending on espionage, and if the targer tace has techs you don't, there's a small chance that is based partly on your espionage spending to steal one of those techs.
~SDC~