Passkeys

It sounds like you're doing everything right, but let's break down what's happening and clear up any confusion about passkeys.

Here's how passkeys work and why you're seeing what you're seeing:

Passkeys are based on public-key cryptography. When you create a passkey, a pair of keys is generated: a private key and a public key. The private key stays securely on your device (or in a synced cloud service like iCloud Keychain or 1Password) and is never shared. The public key is stored with the online service (like Amazon).  
Multiple devices can have passkeys for the same account. This is a core feature! It lets you sign in to Amazon (or any other service) from any of your devices that have a passkey. Each device generates its own unique private key, but they all unlock the same account.  
Passkey syncing. Services like 1Password and iCloud Keychain can sync your passkeys across your devices for convenience and backup.  

Explanation of your observations:

1Password entry: 1Password is likely updating the passkey entry to reflect the most recently created passkey. This doesn't mean your old passkeys are overwritten, just that 1Password is keeping track of the latest one.
Multiple passkeys on Amazon: You have successfully created two passkeys for Amazon: one on your Windows machine (stored in Firefox and synced to 1Password) and one on your iPad. Both are valid and can be used to sign in.

Answers to your questions:

Is the private key stored in 1Password? Yes, if you have 1Password set up to sync passkeys. This is generally a good thing for backup and convenience.
Did I do something incorrectly? No, you haven't done anything wrong. Creating multiple passkeys is expected and allows for flexibility.
How do I delete the passkeys and start over?
Amazon: Go to your Amazon account settings, find the security or login settings, and look for an option to manage passkeys or authentication methods. You should be able to delete individual passkeys there.  
**1Password: **You can also manage and delete passkeys within 1Password itself.