FineWoven Wallet not appearing in Devices or Find My but says "Not my wallet" when attempting to connect to another device

Goal: Free up my iPhone FineWoven Wallet so I can it gift to a friend and so they can connect it to their Apple account.

Issue: When I attach the wallet to another iPhone, it says "Not my wallet". The wallet does not show up in my Find My device list, nor does it show up in my Devices in my Apply account. I only have one Apple account, so it cannot be attached to another account.

Background: I purchased the wallet after getting an iPhone 16 Pro, and after a couple of weeks I decided it wasn't for me and I returned the iPhone. I set up the Wallet while I had the iPhone 16 Pro, and I don't recall if I disconnected the wallet beforehand. I don't know if this is relevant, however, and I couldn't find any support material saying that this would be an issue.