Do I need to file a 90-day report after reentering Thailand on a NON-O visa?

You've got some of it correct

You do a 90 day report once you've been IN the country 90 continuous days on a visa/extension.

Your initial 90 day report would have been due 89 days from the date you applied for the year extension so mid August sometime (they usually put a small paper IN your passport telling you when the first report is due)

However you said you traveled before that and returned on Aug 3 <- meaning if you don't leave the country your NEXT 90 day report would be due Oct 31st

You can leave the country for as long as you want to as long as you're back before the current extension expires so you can apply for another one..

90 day reporting has nothing to do with your extension, it's just something you have to do if you're in country 90 days at one time.