I currently have a 2nd generation Apple TV
You probably meant the 2nd gen Apple TV 4K, as the 2nd gen ATV is now 14 years old.
Over time, many of the apps on the home screen no longer work. For instance if I click on TED it says it is not available, try again later.
I almost guarantee that this has more to do with developers no longer supporting tvOS version of apps rather than the version of Apple TV that you have is old.
unless something has changed recently, there are hardly any apps that are unsupported on one tvOS ATV that will work on a newer tvOS ATV. For example, the Apple TV 4 (HD) that came out in 2015 when tvOS launched will be compatible with 99.9% of the apps that the newest 2022 ATV4K3 can play.
There are a few apps that might not be compatible, most, if not all, are games.
My question is whether that's common to all generations of Apple TV, including the current one, or is the unavailability of the apps due to the age of my unit?
It is most likely due to the developer no longer supporting tvOS. Basically, Apple is driving away what little tvOS developers there were.
tvOS has been hemorrhage third party developers for a while now. I made a thread about it a few years back when SMG, the maker of the iOS and tvOS game RISK, stop supporting the tvOS version of it. Evidently, Apple has made development on tvOS very difficult, and considering that Apple lost a huge amount of the streaming box marketshare over the past 10 years, there isn't an incentive to develop and support tvOS version of apps.
This is most likely what is happening to TED and your other apps that no longer work.
I have so many apps on my 2015 ATV4 that have been abandon by the developers. Some can't be downloaded anymore. Some can still be downloaded, but no longer work. Some can be downloaded, opened, but not fully used because it is broken.
I was hoping that Apple would turn it around, but they never really seem to have any interest in ATV since the launch of tvOS.