Will factory reset from xbox one effect xbox one S on same account?

No. Factory resetting a console won't affect anything on another console.

hi,

try to make a factory reset with the option to keep your data. you need your login information.

https://support.xbox.com/xbox-one/console/reset-console-to-factory-defaults

I think the factory reset will not work. I came from an Xbox S for Xbox X, and the problem was already on Xbox S.

I think the problem is not linked to the console, but apparently in the account.

If you remove your account from the console and reset your console to factory defaults on Xbox One (chose reset and remove everything) nothing will remain from your saved data or downloaded games in the said console.

To remove your account from console:

support.xbox.com/.../remove-profile-from-console

To reset your xbox one console to factory settings:

support.xbox.com/.../reset-console-to-factory-defaults

Hi there!

If you've tried it on another Xbox with the same account then I suggest to
soft factory reset your Xbox One X. If the game still doesn't work after a factory reset then you would need to re-install the game again. The Xbox Live Services are up and running and I'm not familiar with that specific error message as it might be from
the game.

Try out the soft factory reset and let us know the results!

I understand, have you performed factory reset on both consoles? If not yet, please try to perform the factory reset keep my games and apps on your Xbox One S console > then check if it works.

If it still doesn't work, may I have the exact error message upon attempting to log in to your accounts on your Xbox One S, please?