Hotside aeration is another one of those brewing bogeymen that is only of concern to large commercial breweries brewing lagers (think BMC where
any flavors, off or otherwise are considered a no-no.)
It is really nothing a homebrewer needs to stress about.
What you did is the same as whirlpooling your hot wort to clump it all in the bottom of your kettel...Use the search feature an look up whirlpooling...
In other words you did nothing different than many of us do on a regular basis while cooling our wort...It will be fine....I rock mine back and forth every now and then, and even lift it out of the sink to swamp out water, and my beers are fine.
If you took an electric egg beater and beat your wort into a froth, that
might be a different story...But remember, your beer
Needs Oxygen anyway....
so don't sweat these brewing issues that you hear about, or read about...most of them are only of concern to large scale brewers,
not us humble homebrewers....They just get repeated over an over like that old game we played as a kid called "telephone," until they become the stuff of nightmares for beginning brewers.
I wrote a blog about this a few weeks back....I wish
some people would read it before they jumped in and posted certain things in threads like this...
https://www.homebrewtalk.com/blog.php?b=50
My bigger concern would be that you didn't sanitize whatever you used to stir the wort as it was cooling.....Either keep a spray bottle or bowl of sanitizer handy and sanitize each time you remove the stirrer...or, I usually just leave my brew paddle in the kettle from boil all through the cool cycle....that way it stays as sterile as the wort is....