Based on the provided information, it seems that the InnoDB engine is failing to register, causing the initialization of plugins to fail, and ultimately resulting in the inability to start MySQL. Additionally, the error log shows that the MyISAM, CSV, and keyring_file plugins are also shutting down.

When attempting to login through the SQL command, the error message indicates that the local MySQL server cannot be accessed through the specified socket. This could be due to a misconfiguration in the mysqld.cnf file.

Furthermore, when trying to restart MySQL, additional errors are encountered. It is difficult to determine the specific cause of these errors without further information, but it may be related to the initial issue with the InnoDB engine failing to register.

To resolve this issue, it may be necessary to review the configuration files and settings related to the InnoDB engine, as well as checking the permissions and ownership of the files and directories involved. It may also be helpful to review any recent changes made to the server or to the MySQL configuration that could have caused the issue. Additionally, consulting MySQL documentation and forums for similar issues may provide helpful insights and solutions.