Odd redirection when I try to change Apple ID

Hello JespertheGreat,

The first solution is not to choose your default Apple ID when you connect to appleid.apple.com. Choose instead “other account” (or something to that effect). You’ll then be prompted for an Apple ID (use yours) and a password (yours). Your Mac will then ask you to confirm your identity with a 6-digit code sent to your other Apple devices. Once logged on, you’ll have no issue making changes to your account.

The second solution is to use another browser such as Firefox: https://www.mozilla.org/en-US/firefox/.

See this Apple article: Change your Apple ID -> Change your Apple ID - Apple Support (SG)

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If you can’t change your Apple ID

If you're trying to change your Apple ID to an @icloud.com email address that was created within the last 30 days, you will be asked to try again later.

If you see a message informing you that the email address you want to use isn't available or is already in use, check that you or a family member isn't already using that email address with a different Apple ID. If a family member is using that email address, remove itfrom their account, then try to use it. 

In some countries or regions, you can use your phone number as your Apple ID. But if your Apple ID is an email address, you won't be able to change it to a phone number.

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You are sign in here .  .  .  with your Apple ID & Password.

Your Apple ID is the personal account you use with all Apple products and services. It includes the email address and password you use to sign in, as well as the contact, payment, and security details that you use with Apple.

You can’t merge multiple Apple ID accounts.

See the following Apple articles

Sign in with your Apple ID -> https://support.apple.com/en-us/HT204053

Manage and use your Apple ID -> Manage and use your Apple ID – Apple Support (UK)

an old company email to my new email,  

You cannot change that old company email to your Apple ID that you use to sign in here.

I am going through the motions of changing my Apple ID away from an old company email to my new email,

No, that is not possible.

If you no longer work for that company, that company has already deleted your work email address. This is done as soon as you have left the company so that you can no longer log in. You no longer have any rights there.

An deleted email address, it is no longer valid, it simply no longer exists and it no longer works.

You may not be able to change that email work address because it is no longer exists.

You are most welcome, JespertheGreat! Have a great weekend!