How did I fix «This email address is not available» for Apple ID?

I have 2 Apple ID accounts:

  1. apple.5857@yandex.ru
  2. dfediuk2@gmail.com
    The second account previously was linked to another email address: dfediuk@gmail.com
    I have re-linked the account to dfediuk2@gmail.com today.
    Now, the dfediuk@gmail.com email address is not used as the primary nor as a recovery email address for any Apple ID.
    I want to re-link the first Apple ID account from apple.5857@yandex.ru to dfediuk@gmail.com, but the system forbids me to do it: «This email address is not available».

This email address is not available. Choose a different address.

2023-08-13--08-18-38

The same question:

Some articles from support.apple.com (they do not explain the problem)

It seems to be impossible:

You can’t remove the primary email address associated with the account.
You can set another one as the primary, but the first email address that you use to create the account with cannot be changed ever.
Not even by calling Apple.
I tried.
Eventually, I created a dummy gmail account to get my invoices and stuff.
Once an email address is verified, there is no way to “unverify” it.

apple.stackexchange.com/a/62482

Iterestingly, the «Forgot Apple ID or password?» / «Having trouble signing in?» page (iforgot.apple.com/password/verify/appleid) shows: «This Apple ID is not valid or not supported»:

2023-08-13--14-22-39

I found a solution!

Step 1

Add the email address which you want to use as Apple ID (dfediuk@gmail.com in my case) to «Personal Information» → «Reachable At»:

2023-08-13--14-48-00

Step 2

Now you can switch your Apple ID to this address:
2023-08-13--14-47-05

2023-08-13--14-47-32