I have just tried to change my sign-in Email but have not received a confirmation email

Thanks for the confirmation/clarification, @STHK888.

So I would actually recommend doing something different at this point -- you've gone through this process and for some reason, it's stuck or broken or stubborn - or all three!

Here's my recommendation in a few simple steps.  I'll refer to Email A as the current owner, and Email B as the desired/future owner.

1. On the Zoom Web Portal, using Email B, create a Zoom account separately.  A Basic, unlicensed/free account.  Log out of the Zoom Web Portal.
2. Log into the Zoom Web Portal using Email A.  Click on Admin -> User Management -> Users.
3. Click the blue +Add Users button.  In the window that pops up, add the address of Email B.  Click the "Basic" radio button for User Type.  Click the Add button.
4. Within a few minutes, Email B will receive a request to join the account of Email A. 
5. Log out of the Web Portal (Email A) and log back in as Email B.
6. Click the blue Approve the Request button in Email B's invitation.
7. Log out of the Web Portal (Email B) and log back in as Email A.
8. Go to the Admin -> User Management -> Users menu and see BOTH Email A and Email B are on the account, since Email B has accepted the request to join Email A's "organization".
9. On the Email B account line, click Edit at the end of Email B's line.  On the Edit User screen, change the Email B account's role to Admin and press Save:
   
   Note: The candidate must be an admin before they can be made the owner!
10. Still logged in as Email A, go to Admin -> Account Management -> Account Profile.
11. Click Change Owner:
    
12. You will be prompted for your password for the Email A account.  Enter it and click Continue.
13. When prompted for the email address of the new owner, enter Email B. Click the Change button.

VIOLA!  Email A is now an Admin on the account, and Email B is now the account owner.

See these Zoom Support articles for additional details on this process:

https://support.zoom.us/hc/en-us/articles/360028938451-Adding-existing-users-to-a-paid-account

https://support.zoom.us/hc/en-us/articles/115005686983-Changing-the-account-owner 

I never recommend transferring ownership to someone external unless two organizations are joining together (merging).  I always recommend giving ownership to someone established on your account.  Establishing a new account member or transferring someone into your account isn't usually difficult.

NOW... don't do anything else until you've answered this question:

What do you want to happen with Email A's account?  Do you want that email address and it's account to GO AWAY?  Or do you intend to keep two accounts?

If you want Email A to GO AWAY, there is a process to delete a user and transfer all the user's assets (meetings, recordings, etc.) to an existing user.

See this article which describes how to DELETE Email A's account and transfer assets over to Email B's account:

https://support.zoom.us/hc/en-us/articles/115005866183-Transferring-data-to-another-user 

Read it carefully; my experience with this is limited.  I've heard horror stories of people who have deleted a user without transferring, and then wondering where their assets went... and they're gone - that's all I can say.

So... hopefully this gives you a path to go down to transfer the ownership from Email A to Email B.