You’d have to type in your instance name upon tapping the button
You could have a settings page that lets you set your instance name and then twitch (or whatever service you’re using would store that along side your other user data)
It just assumes one of the most popular instances.
But without some central registry there’s no way to know what is your home instance.
Edit: something like what Android does for Activities could work as well. But not sure how to handle that on a PC. … In Android they could just start a generic Intent to view Lemmy and it could then launch whichever app you have installed to handle that intent.