Apple ID OK and password but no Recovery Key on my old devices

Using the same Apple ID on your newer and older devices the Apple ID itself can only be one type of account (like Two-Factor Authentication).

However, even older devices that don't understand Two-Factor can still use the same Apple ID.

To sign onto an Apple ID that has been upgraded to Two-Factor on an older device that doesn't understand Two-Factor you have to put in the verification code as part of the Apple ID password.

So if you have a modern device such as an iPhone X, with an Apple ID with two factor, you would just sign on as normal. Let's say your password is My#1Password. But on your old device, such as an iPhone 4, or Classic iPod, or anything running iOS 8 or older, you would put in the password+the verification code received on your Trusted iPhone X, such as My#1Password012345 (if 012345 was the verification code).

See the section "What if I use two-factor authentication on a device running older software?" here: https://support.apple.com/en-us/HT204915

Sorry, no. Two-factor (or two-step) authentication is associated with your AppleID account - and can be one or other, but not both.

Once two-factor authentication is enabled (as is required for many Apple services), you have a very short window of time in which to revert to two-step authentication - after which it is impossible to return to the older (now deprecated) authentication system.

You might try, but use of two AppleIDs has other implications - and a new AppleID account, when created, will not offer two-step authentication.

As already stated, two-step authentication has been deprecated; most Apple Service require two-factor authentication to function.