Are the Xbox Avatar items still ongoing including the program I am no longer with?

I see. Anyway, it's probably a good thing I moved on.

There has been no official word on Avatars being shut down so it will continue for the time being. The Ambassador program has not given away avatar items for a while now.

As I mentioned it does not include in-game or avatar items. Personalization items such as skins, etc or items specific to your avatar are not included.

The answer is yes and no. Yes, your 360 Avatar items moved with you when you went to Xbox One. And also no because the new avatars that recently came online can no no longer use anything from the previous Avatar generation. To avoid confusion I am going
to refer to them and and their respective avatar editor with the designation of 1 and 2. What they have done is allow you to import Avatar 1 into Avatar Editor 2 in order to continue to use Avatar 1 and not lose all the clothing and items people have purchased.
So use Avatar Editor 1 to setup avatar 1 however you like. Then use Avatar Editor 2 and import Avatar 1 into the new system. Now you won't have all of avatar 2's functionality but you will still have your old items. They just had no way of making the old items
fit the new avatars because body types and height etc were now so customizable. I encourage you to play around with both systems to find out what works for you. Your 360 items will be found in avatar editor 1. Hope this helps.

Any purchased item is linked to the account. This includes games, DLC's and avatar items that you purchased.

Avatar items that were earned via gameplay may not be retrievable.