I purchased a new 2nd Generation Apple TV and installed it today. I didn’t receive a notification for free 1 year of Apple TV

If you have had the Apple TV+ subscription before, then your wouldn’t get the offer. One offer per user or family.

If you are eligible, then a notification isn’t needed to redeem the offer.

Read here how to redeem: Apple TV+ offer - Apple

Read here about the conditions: Apple TV+ offer - Terms and conditions - Apple

Read here if you have trouble redeeming: If you can't redeem your promotional trial of Apple TV+ - Apple Support

the appletv 2nd g was released in 2010 and was discontinued in 2012

Well, first of all, the offer is no longer 1 year but 3 months. That changed July 1, 2021. No more 1 year trials.