start-on-macos

ref (unreliable): https://stackoverflow.com/questions/15450091/error-2002-hy000-cant-connect-to-local-mysql-server-through-socket-tmp-mys

Download dmg from official. Something like https://cdn.mysql.com//Downloads/MySQL-8.3/mysql-8.3.0-macos14-arm64.dmg .
Run the dmg. You will have cli tools then, now you have:

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~ λ mysql --version
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mysql  Ver 8.3.0 for macos13.6 on arm64 (Homebrew)

brew services start mysql or something else to start mysql service.

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==> Successfully started `mysql` (label: homebrew.mxcl.mysql)

mysql_secure_installation
Next, see the following history:

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~ λ sudo mysql
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Password:
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ERROR 1045 (28000): Access denied for user 'root'@'localhost' (using password: NO)
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~ λ sudo chown -R _mysql:mysql /usr/local/var/mysql
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chown: /usr/local/var/mysql: No such file or directory
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~ λ sudo mysql.server start
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Starting MySQL
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. ERROR! The server quit without updating PID file (/opt/homebrew/var/mysql/floriandeMacBook-Air.local.pid).
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~ λ mysql -u root -p h127.0.0.1
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Enter password:
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ERROR 1049 (42000): Unknown database 'h127.0.0.1'
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~ λ mysql -u root -p
15 collapsed lines
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Enter password:
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Welcome to the MySQL monitor.  Commands end with ; or \g.
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Your MySQL connection id is 12
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Server version: 8.3.0 MySQL Community Server - GPL
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Copyright (c) 2000, 2024, Oracle and/or its affiliates.
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Oracle is a registered trademark of Oracle Corporation and/or its
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affiliates. Other names may be trademarks of their respective
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owners.
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Type 'help;' or '\h' for help. Type '\c' to clear the current input statement.
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mysql> CREATE USER 'julyfun'@'localhost' IDENTIFIED BY 'guest123';
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Query OK, 0 rows affected (0.03 sec)

You can now install, in vscode, the MySql extension by Wejian Chen.

Better not

brew install mysql / mariadb