Hi @cee_em,
Currently you are unable to install custom or draft apps on client transfer stores. This is described in the Shopify.dev documentation:
You can’t install custom or draft apps on client transfer stores. Create a dev store in the Dev Dashboard to build and test your app.
In this case you should be transfering the store first, then if you need to create a custom app on the store you can do so after it’s transferred, with a collaborator account, or have the merchant create the custom app in the Dev Dashboard and provide you with the Client ID and Client Secret, to use with the Client Credential Grant Workflow to create an access token for use.
Additionally it is very important to know that you can not install the same app on multiple merchant stores as a custom app. If you are installing the same app on multiple stores, it is required that the app is released as a Public app and does have to go through our App Review Process, though you can leave it as unlisted so only merchants that get the link to install it from you directly can use it.
API Restrictions. When using the Shopify API, you will (and will ensure that your employees, agents and service providers will):
…
not make Custom Applications available to or for use by more than one Merchant. For the avoidance of doubt, this means that Custom Applications may not be installed by more than one Merchant. For clarity, a Merchant may have more than one Merchant Store.