Xbox 360 Account not Working On Series X

Just some additional information you should be aware of:

The Xbox 360 and the Xbox 360 emulation software on the Xbox One and Series X is quite fussy with passwords. It may display an error with passwords that it has issues with, even if these passwords work fine on the main account of an Xbox One or Series X console.

• Keep your password to less than 11 characters.
  
• If your password has special characters (such as !"%@~#) these can cause issues. Also passwords with spaces can also have problems.
  

Bear in mind there is no such thing as an Xbox 360 account an Xbox One account or a Series X account. Your Microsoft/Xbox account will work on all Xbox Online services on different consoles and PCs.

Elaborating slightly: None of our family accounts on the same xbox aside from mine have xbox live gold (ultimate in my case). Previously on xbox one x, for instance, my wifes xbox account, she would sign into MWF3 360, go to live and join games. Now on
xbox series X, same exact steps, it throws the error. You could always play under other accounts as long as one account was a live paid account (360 or regular xbox one x titles), now it only works for one x or one x series x titles.

Subscriptions are related to your account - so it will work with 360, One and Series X/S !

The 'App password' for the Xbox 360 is a work-around for the two step verification system available for the Xbox One/Series X|S. As the Xbox 360 doesn't support 2 step, you need to use an 'App Password' on these consoles.

For the Xbox One and Series X|S consoles, you need to use your Microsoft account password.

Xbox One, Xbox One S, and Xbox One X controllers work on Xbox Series X|S, and vice versa. However, Xbox 360 is on it's own, similar to the OG Xbox.

What's cool however is if you remote stream Xbox One, One S, One X, Series S, or Series X on, say, a PC, you can plug in a 360 controller and use it on the newer generation.

But no, newer controllers aren't supported on 360.