The Joy-Con can be paired to one console at a time. If you wish to use the Joy-Con on another console, they will need to be paired to that console.
How to Attach/Detach the Joy-Con Controllers from Nintendo Switch
Applies to: Nintendo Switch Family, Nintendo Switch, Nintendo Switch Lite, Nintendo Switch - OLED Model
In this article, you'll learn how to attach and detach the Joy-Con controllers to the Nintendo Switch console.