How do I transfer a Minecraft world from one device to the other with the same account?

Really the only way to do this is to use the in-game Realm service to move the world. Just warning ahead of time, this costs REAL money to use. If you upload a word to a realm, you have the option to download that world on any device. Handy if you have multiple worlds you would like to transfer between devices (not limited to just Switch and Xbox). On the other hand, if you have just one world, and don't mind paying for the subscription, you can just leave the world in the realm and have a way to access it without the process of uploading, then downloading every time you switch devices. The only downside to that is you need to be connected to the internet to play on a realm.

(This is one of my first answers. Please let me know how I can improve.)