A Microsoft app for iOS and Android devices that enables authentication with two-factor verification, phone sign-in, and code generation
You're confused about what a passkey is versus a Windows Hello PIN, which is one of many issues we see when consumers try to understand security concepts as complex as passkeys, since the true security in their case is based on public key cryptography, with the private key stored in your device and the public key store on the website you're trying to access.
In other words, the Windows Hello PIN is merely a quick unlock method you use from your personal device, which can also be done using Biometrics like Windows Hello Face (camera) or Fingerprint when either of those physical devices are included with the device, which is becoming more common to make the process easier and faster.
You're correct that the passkeys themselves are associated with each remote website, including login.microsoft.com, which is the primary passkey you actually use when you login to your device using your PIN, since Microsoft stopped using your Microsoft account password to do this quite a few revisions of Windows back, instead storing a passkey for your account and using that when you successfully type your PIN in its place, since that's a much safer method.
The problem you're seeing with your wife using your same "4444" PIN to login to access Amazon, or in truth really the device itself, is actually another common issue which how many people use their Windows Devices today, since you're really logging into Windows itself with a single account, whether that's your own personal Microsoft account like CRobinson@ Microsoft.com or a local account named something else entirely. In this case, you'll need to evolve to using the separate personal Microsoft accounts you already have to login to the device, with each of you having your own initial login to the device(s) you use, with your own personal desktop and other information.
The other possible way to do this is by using your personal smartphones if you each have one to carry your passkeys with you at all times, storing them in an authenticator app on that device and using them both at home and wherever you might be where you want to access your accounts including possibly email, banking, etc. This way, you can still have a single login using a local account at home if you prefer (though Microsoft and I would still recommend using your separate Microsoft personal accounts for this for multiple reasons) along with the ability to 'take your passkeys everywhere', using your smartphone to, for example, access your email or online banking from your device at work if that's allowed, or gain quick access from a friend's home PC when you're visiting if you trust that those devices you're using are otherwise safe for the purpose.
The other point I should make is that Windows 10, which I also use at present, isn't as easy to use with passkeys for several reasons, including that unlike my own Microsoft Surface Go tablet that came with came with Windows Hello Face (and PIN), many older upgraded devices only have the PIN, so they're less easily logged into quickly the now relatively many times daily you'll need to do this. Windows 10 also doesn't have the passkey manager app that Windows 11 does, so troubleshooting or deleting outdated or problematic passkeys there isn't easily possible, making passkeys less friendly when used on those older devices.
For the above reasons, along with an initially flakey set of problems trying to set up my first Amazon passkey login when I didn't understand some of this myself, I've decided to wait until I get a new Windows 11 system to start using passkeys, since the problems I had were mostly due to no visibility and thus no way to troubleshoot with Windows 10.
The other thing that's different when using the smartphone to store and access you passkeys is that instead of using your PC device's keyboard to type your PIN, you'll be using the camera, fingerprint reader and/or PIN on that phone device instead, which if that has at least one Biometric makes that 'cross-device' authentication method relatively easier, though of course your smartphone must be present when needed for that access.
Note that sine the PIN (or Biometric) relates to the device in use and not the passkey itself, those PIN's might be entirely different for both you and your wife just as your stored pictures or fingerprints would obviously be as well, since those are associated with that device in order to 'unlock' both your device and also the passkeys they contain when needed.
Hopefully, this starts to give you an idea how these objects all relate to one another and why people get confused, since the Private keys stored within the TPM (or similar encrypted hardware chip on a smartphone), never actually leave the device itself and are instead used during a challenge/response interaction with the website to create a temporary passkey that's actually what's being sent back and forth during the authentication process, meaning the most critical information stored in your PC or phone device never really leaves, only the public key provided to the website when you first create the account relationship between them and the initial encrypted communication process used to set up the relationship.
See why I stated this system is actually so complex, but once set up with a particular website, as easy to use as simply typing your PIN (or entering your Biometric) into the specific device that contains your passkey, or actually your private key that's used to create it?
It's a truly beautiful and secure system once in place and you understand the basics of how to use it, but without at least some basic understanding of how it flows, its exceedingly difficult to understand, since most people want at least some level of understanding to feel comfortable using it and the invisible private keys, and other highly technical objects flying around between your device(s) and the remote websites are nearly impossible to understand without some form of this description.
Rob