hostの番号が合わないです。、terminalde,mysqlが実行できない。

Question

前提・実現したいこと

hostのエラーを改善して、terminalでmysqlを実行できるようにしたい。

発生している問題・エラーメッセージ

,1ターミナル。
mysql.connector.errors.InterfaceError: 2003: Can't connect to MySQL server on '127.0.0.1:3306' (61 Connection refused)
2,いつもの画面
(base) SN:toudai SN$ sudo mysql.server start
Password:
Starting MySQL
. ERROR! The server quit without updating PID file (/usr/local/var/mysql/SN.local.pid).
(base) SN:toudai SN$ mysql -u root
ERROR 2002 (HY000): Can't connect to local MySQL server through socket '/tmp/mysql.sock' (2)
(base) SN:toudai SN$ 

該当のソースコード

ターミナルの方です。
The default interactive shell is now zsh.
To update your account to use zsh, please run `chsh -s /bin/zsh`.
For more details, please visit https://support.apple.com/kb/HT208050.
(base) SN:toudai SN$ ls
data.py         main.py         mysite          test_sqlite.db  venv
(base) SN:toudai SN$ 
(base) SN:toudai SN$ cd vnev
bash: cd: vnev: No such file or directory
(base) SN:toudai SN$ cd data.py
bash: cd: data.py: Not a directory
(base) SN:toudai SN$ 
(base) SN:toudai SN$ mysql -h X.X.X.X -P 3306 -u wordpress -p
Enter password: 
ERROR 2005 (HY000): Unknown MySQL server host 'X.X.X.X' (0)
(base) SN:toudai SN$ 
(base) SN:toudai SN$ show variables like 'port';
bash: show: command not found
(base) SN:toudai SN$ 
(base) SN:toudai SN$ mysql -u root
ERROR 2002 (HY000): Can't connect to local MySQL server through socket '/tmp/mysql.sock' (2)
(base) SN:toudai SN$ 
(base) SN:toudai SN$ sudo mysql.server start
Password:
Starting MySQL
. ERROR! The server quit without updating PID file (/usr/local/var/mysql/SN.local.pid).
(base) SN:toudai SN$ 
(base) SN:toudai SN$ mysql -u root
ERROR 2002 (HY000): Can't connect to local MySQL server through socket '/tmp/mysql.sock' (2)
(base) SN:toudai SN$ 
(base) SN:toudai SN$ brew uninstall mysql
Uninstalling /usr/local/Cellar/mysql/8.0.23... (298 files, 297.8MB)
(base) SN:toudai SN$ brew install mysql
Updating Homebrew...
==> Auto-updated Homebrew!
Updated 3 taps (homebrew/core, homebrew/cask and mongodb/brew).
==> Updated Formulae
Updated 19 formulae.
==> Updated Casks
Updated 14 casks.

==> Downloading https://homebrew.bintray.com/bottles/mysql-8.0.23.big_sur.bottle.tar.gz
Already downloaded: /Users/SN/Library/Caches/Homebrew/downloads/3fb6af4a674bc868f1e2234f3109496004ef05053a7b2a2ce278b2c0997bcbe5--mysql-8.0.23.big_sur.bottle.tar.gz
==> Pouring mysql-8.0.23.big_sur.bottle.tar.gz
==> Caveats
We've installed your MySQL database without a root password. To secure it run:
    mysql_secure_installation

MySQL is configured to only allow connections from localhost by default

To connect run:
    mysql -uroot

To have launchd start mysql now and restart at login:
  brew services start mysql
Or, if you don't want/need a background service you can just run:
  mysql.server start
==> Summary
????  /usr/local/Cellar/mysql/8.0.23: 298 files, 297.8MB
(base) SN:toudai SN$ 
(base) SN:toudai SN$ sudo mysql.server start
Starting MySQL
.. ERROR! The server quit without updating PID file (/usr/local/var/mysql/SN.local.pid).
(base) SN:toudai SN$ 

import mysql.connector

conn = mysql.connector.connect(host='127.0.0.1')
cursor = conn.cursor()
cursor.execute(
    'CREATE DATABASE test_mysql_database'
)
cursor.close()
conn.close()

試したこと

terminal=>
,調べたを参考に
１，

sudo mysql.server start
mysql -u root

２，

mysqlをけして、ダウンロードしました。

補足情報（FW/ツールのバージョンなど）

pycarm,最新のios,mac

ここにより詳細な情報を記載してください。