My guess is, then, that Apple will allow pre-existing "relationships" between email clients and their servers to remain active with the passwords that were in force at the time the relationship was formed until and unless you go in to manually change them to match whatever you've set for your Apple ID. Then, if you do that, then go back and change your Apple ID password again, they'll probably keep working.
I personally find this system bizarre, but you can do the same thing with a Microsoft Account and the Microsoft Account linked Windows 10 User Account. If you change the password on your Microsoft Account, you can still use the old one on Windows 10 until or unless you were to enter the new one you've set at microsoft.com. If you do that then the old one will be supplanted. But I can understand this for logging in to a machine, because if you were to be offline you absolutely must have some way of allowing a user to log in and that means having a local copy of the password, which is what gets used if you're offline or used first if you enter it correctly even if you're online.
Brian - Windows 10 Pro, 64-Bit, Version 2004, Build 19041
Always remember that computers are just glorified light bulbs - they rarely fail in continuous use and usually go pop when turned off and on.
~ Technician with the username Computer Bloke, on Technibble.com