New Country - Too many verification codes have been sent. Enter the last code you received, use one of your devices or try again later.

The standard way of doing things with Apple is one account per user, with that account set to the user's country of residence. Once you start doing things differently, I don't know how the system responds. If your UK number works in Poland, you should be able to receive codes via SMS. If it does not work then that may be the issue. Apple will try to send codes via the Internet to trusted devices too, so if you are getting them for your personal account that way, that may explain why you are getting codes for it but not for the other devices. They are not signed into the same account and your personal phone is not "trusted" by them for regular Apple notifications, just for getting codes by SMS which isn't working.

Unless you have a very old account and only recently set up 2FA, you cannot disable it. See Two-factor authentication for Apple Account - Apple Support

I don't use 2FA (my account is very old) so I have never received a code and I don't have firsthand experience in how it all functions. Read this link about trusted devices. Two-factor authentication for Apple Account - Apple Support - "A trusted device is an iPhone, iPad, Apple Watch, Apple Vision Pro, or Mac that you’ve already signed in to using two-factor authentication. It’s a device that we know is yours and that can be used to verify your identity by displaying a verification code from Apple when you sign in on a different device or browser."

“Two-factor authentication requires iOS 9 or later, OS X El Capitan or later, or iCloud for Windows 5 or later.”

and

Get a verification code and sign in with two-factor authentication - Apple Support

"A code is sent first to your trusted devices automatically. If you have a trusted device running iOS 9 and later, OS X El Capitan and later, iPadOS 13 and later, or watchOS 6 and later, the verification code is displayed automatically on your trusted devices."

As long as you have a device that is signed into the same account for which a code is being requested, it should receive the code. Typically if you do not have multiple devices signed into the same account, it is a good idea to have multiple numbers (friends or family) who can get a code for you, or a recovery contact.

Similar information for the iPhone can be found here --> Use two-factor authentication for your Apple Account on iPhone - Apple Support

If you had set up an Account Recovery Contact ( Set up an account recovery contact - Apple Support ) you can also get a code that way.

Finally, if you have relocated to Poland to take up residency, you should change countries (and telephone service) on your account. Change your Apple Account country or region - Apple Support