Older No Man's Sky Game save gone while newer one is still available, how can I get it back...

Since the game is not available for the One, there's no way to play it on that consoles. The console will still get some updates, but it's the older generation of consoles so there will be newer games that are not released for it.

On the account where the corruption occurred, navigate to C:\Users\NAME\Saved Games\GAME where NAME is your username and
GAME will be something like No Man's Sky in this case. Rename the No Man's Sky folder to something like No Man's Sky - Bad. Launch the game and see if it acts differently.

It seems No Man's Sky doesn't create a save there. I did find local save data elsewhere and deleted it, but the corrupted profile still doesn't work.

It will but not as much. I was back on the MW2 servers not too long ago and had no issues.

I do like the fact that the cheaters still get banned while playing the older cod's.

I guess they think they only watch the newer games.

I resolved this. I was able to delete the local files and restore from the cloud. Phew! I actually have 900 hours in this game on my Xbox and I still have not yet reached the center of the galaxy. To busy exploring and finding new things to explore and do. Here are some solutions that I found:

A. Try deleting the local save data for No Man's Sky and then syncing it with the cloud. To do this, follow these steps:

1. Press the Xbox button to open the guide.

2. Select My games & apps > See all > Games.

3. Highlight No Man's Sky and press the Menu button on your controller.

4. Select Manage game and add-ons > Saved data.

5. Select Delete all to remove the local save data for No Man's Sky.

6. Once the local save data has been deleted, restart your Xbox console.

7. When your Xbox console has restarted, open No Man's Sky and allow it to sync with the cloud.

8. Once the sync has completed, try loading your game save.

Or…

B. Try joining someone else's game. If you are able to join someone else's game, your save file may be able to load correctly. Once you have joined someone else's game, try saving your game and then quitting the game. After you have quit the game, try loading your save file again.

Or…

C. Use a save editor. There are a number of save editors available for No Man's Sky. These editors may be able to fix your corrupted save file. To use a save editor, you will need to copy your save file to your computer. Once you have copied your save file, you can open it with the save editor and try to fix the corruption.

You can get a save editor for No Man's Sky on the Xbox from the GitHub repository of goatfungus. The repository is here: https://github.com/goatfungus/NMSSaveEditor

Or…

D. Contact Hello Games support. If you have tried all of the above solutions and you are still unable to load your game save, you can contact Hello Games support for help. You can contact Hello Games support through their website: https://hellogames.zendesk.com/hc/en-us.

I didn't claim you were, lol, but is it the newer Xbox 360 Slim or is it one of the older models? You can see if it has been opened if the warranty sticker on the older models, under the faceplate is still there, or on the newer models, on the very back.
Check that to be safe.