I changed my gamertag but now when I try to play Xbox 360 games they won't allow me to sign in

That is because if you aren't using alphanumeric characters or include symbols it won't recognize since its based on ansi

Your forum name is too long

You must use classic name on old games

Each 360 account can be associated with a Live account.

Currently I have:

old 360 account -> associated with my Live account but with the old gamertag

new 360 account -> associated with my Live account but with the new gamertag

The new account got created when I downloaded my profile using my microsoft sign in. The old account was associated with the same microsoft sign in but it didn't recognize my gamertag change. Now it won't let me sign in to live because it asks for my microsoft
sign in details. I'm guessing the sign in fails because it's trying to find the microsoft account associated with the old gamertag.

I either need to somehow transfer my saves over to the new 360 account so I can upload them to the cloud, or I need someway for my Xbox to realize that my gamertag changed on the old account so I can sign into live again with that account.

I recently changed my gamertag on xbox one and made a longer password now when I go to play a 360 backwards compatible game on xbox one it says I have to re download profile so my gamertag will change but my password for live is too long on 360

But the gamertag that I want to change is my old gamertag. I change my old gamertag on 2 August 2020. I used that old gamertag when I create my Xbox account. At that time, the system allow me to use that gamertag. But when I want to change it back, the system don't allow me to use it. Why is this like that?

It now allows me to play for short periods of time, and then randomly signs me off. When I restart my Xbox and try to log in again, it tells me that a problem occurred while signing in.