How does a database use the SYS schema even when we change the password? From the thread What is the difference between sys and system accounts in Oracle databases?, I understand that sys schema is supposed to be used only by the database.

But still an administrator can change the password for the schema.

Can the database connect without the password? If not, how does it connect even after the password is changed?
The database doesn't bother authenticating itself to itself.

As the database does not use the password identification strategy when performing operations, changing the SYS password only impacts how humans can use the account.