They dropped the original Xbox like a box of bricks. They shut down those old servers quite rapidly. With the Xbox 360 however, they will stop the ability to buy games on an original Xbox 360 next year. That's a long era of support!
https://news.xbox.com/en-us/2023/08/17/xbox-360-store-will-c...
I'm fairly convinced new credit card standards are probably what is closing down the 360 store. They're only closing down the ability to buy things. Nintendo is also shutting down the Wii U and 3DS around the same time and Sony has already stopped allowing credit cards on a PS3.
https://www.theverge.com/2021/10/6/22713526/sony-ps3-vita-bu...
But getting back to Microsoft, the Xbox One and the Series consoles are running the same store. The OS is for all intents and purposes exactly the same. Any 360 game that has been migrated to the new One/Series store through backwards compatibility is staying purchasable past the closure of the 360 store.
When the next round of closures comes, Microsoft won't close down a store, they'll prevent the Xbox One from accessing the store. I hope with all my might that Nintendo does the same; that the Switch OS remains their software platform and that they close access to their store, not shut it down.