This is sort of where Shopify really dropped the ball. You can only install the link to 1 Org. Otherwise, you'll need to upload it to their public app store, unlist it, and manage it that way. The problem with that is every time you push out an update, you'll need to wait for them to approve it before you can use it.
We ran into the same problem since Shopify didn't have a good answer for us. So, what I did was create a git repo for every extension (see: extension, not *app*), and then created new apps for each Org. Then, from within the Org, I would just clone the extensions. That way, you only need to maintain them in one place.
If you ask me, this is painfully stupid. Lot's of big companies have more than 1 Org. But my experience with this entire Checkout Extensibility has been nothing but horrible. They took away our ability to do anything, and even with the tools they do give us, it's still pretty useless. Want to bold text? Use emphasis='bold' but that's only weight 500, and you can't go any higher so you can barely tell if it's bold or not based on what font you're using. Adding a favicon to Checkout? That requires a 3 different GraphQL mutations which is the dumbest thing I've ever seen.
Checkout.liquid was highly superior in every way to this garbage. Oh, you want more than 20 settings in a single extension? Nope. You want to stack more than 3 extensions together in your Checkout? Nope. You want to use the rich_text_field so you can actually have some way to add links and other text styles to part of your Checkout? Nope.
This is a huge step back, and basically their way of justifying their purchase of Remix.
