Unable to retrieve app-specific password on a different Mac

The important missing bit was app-specific passwords for an Apple Account.

Sign in to apps with your Apple Account using app-specific passwords - Apple Support

You’ll need to sign in separately on each Mac.

To add a bit to what the others have provided you ...

• As neuroanatomist has mentioned, Apple app-specific passwords are tied to your Apple Account, not the device where they were created.
• You can use the same app-specific password on multiple devices if you're setting up the same app (e.g., Outlook or Thunderbird) to access your iCloud email or calendar.
• AFAIK, Apple does not technically prevent reuse, so if you save that password, you could enter it again on a second device or app client — and it will work, as long as it hasn't been revoked.
• I believe what Apple recommends is for you to generate a unique app-specific password for each app or service you're connecting — even across multiple devices. This gives you better granular control when you want to revoke access. For example, if your iCloud account is compromised on one device, you can revoke that one app password without affecting others.

"Unable to retrieve app-specific password on a different Mac: once an app specific password created, I am unable to subsequently retrieve it when using the same app on a different Mac."

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Two-Factor Authentication for App:

If this app is in your Apple Account, then add this Mac as a Trusted Device --you should then get this. Some apps (i.e. Outlook) have THEIR OWN apps for logging in. Go here: Add or remove trusted devices on Mac - Apple Support

See your Devices:

Verify that your Mac is associated to your account, by going here: http://icloud.com/find

How was the password stored? For example, in the Apple Passwords app. If so, both Macs need to be signed into the same Apple ID and Passwords needs to be selected for iCloud sharing on both Macs.

An application specific password is specific to a single app on a single machine. It is not valid when using the same app on a different machine or a different app on the same machine.