I finally decided to upgrade to the 4th gen Apple TV, which I had it as a developer kit about 2 years ago. I had not used it as the gen 2 Apple TV worked out fine mostly of the time, until recently it appears “play on Apple TV” feature did not work well on my old iPad mini (it could be caused by the old router too, oh well, I will replace it one at a time). I recall last time (a year ago) when I tried to use it, the TV comes as dev kit was locked, so I went ahead and did the “restore” in iTunes first. After that the setup was fairly smooth, it seems the main improvement over gen 2 was the voice recognition (Siri) and touch control (the touch control is not as precise as the four way control in the old remote in one case though).
Installed PBS kids app, and the screen saver looks new! Over the weekend I bought some TV from iTunes store (peppa pig, for younger daughter). It showed up fairly quickly on Apple TV.
Now the next step is for me to find the box for the old gen 2 and post it on eBay.