Hello, thank you for reaching out to Microsoft Q&A.
The enrollment wizard for the Extended Security Updates (ESU) program for Windows 10 is rolling out in stages. If you still haven't received this feature, it may become available to your device in the coming weeks as part of the phased rollout.
Once it is available for your device, you can go to Settings > Update & Security > Windows Update to enroll it. (You will see a link to enroll in ESU). So, please wait until it is displayed.
However, it seems that you're having trouble signing in with your account because it is blocked due to repeated unusual sign-in attempts.
Does the user have any other verification methods besides the landline phone number? If you're having trouble verifying your identity, the next option is to reset the security information. To do that, as you mentioned, you will need to get verified by Microsoft after filling out the Account recovery form.
If you're unable to get verified, you will not be able to replace the Security information and close the Microsoft account now. The account will be automatically deleted after 2 years of inactivity.
In this situation, you can try the account recovery form to regain access to your old account or if it fails, create a new account.
Use the new account on the device and make it an Administrator. And, wait for the ESU enrollment wizard to reach your device.
Let me know if you still need more help.