Hi,
The local administrator password changes during the GPO update:
Checks whether the password of local Administrator account has expired or not
Generates the new password when old password expired or is required to be changed prior to expiration
Changes the password of Administrator account
Reports the password to password Active Directory, storing it in confidential attribute with computer account in AD/li>
Reports the next expiration time to Active Directory, storing it in confidential attribute with computer account in AD
Password then can be read from AD by users who are allowed to do so.
For your questions: the computer should update the group policy and read the password expiration information and then generate a new password ,and change the password of the administrator ,then report the password to AD.
Following link for your reference:
https://video2.skills-academy.com/en-us/previous-versions/mt227395(v=msdn.10)?redirectedfrom=MSDN
For the password age (30days by default) ,it can be also changed from the policy.
Best Regards,