mysql can't connect to local MySQL server through socket '/tmp/mysql.sock' (2)エラーを解消したい

Question

前提・実現したいこと

新しくrailsアプリを作成し、
rails db:createを実行したところ下記のエラーが発生しました。

エラーメッセージ
Can't connect to local MySQL server through socket '/tmp/mysql.sock' (2)

試したこと

下記の記事を参考に一度mysqlをアンインストールを行い再びインストールを行いましたが、起動できませんでした。
qita記事

その後、
tail -f /usr/local/var/mysql/*******.local.errコマンドを実行したところ、下記のエラーログが出ている状況ですが、そこからうまく進めることができていない状況です。

021-03-29 18:32:15 73423 [Note] InnoDB: Waiting for purge to start
2021-03-29 18:32:15 73423 [Note] InnoDB: 5.6.51 started; log sequence number 1600607
2021-03-29 18:32:15 73423 [Note] RSA private key file not found: /usr/local/var/mysql//private_key.pem. Some authentication plugins will not work.
2021-03-29 18:32:15 73423 [Note] RSA public key file not found: /usr/local/var/mysql//public_key.pem. Some authentication plugins will not work.
2021-03-29 18:32:15 73423 [Note] Server hostname (bind-address): '*'; port: 3306
2021-03-29 18:32:15 73423 [Note] IPv6 is available.
2021-03-29 18:32:15 73423 [Note] - '::' resolves to '::';
2021-03-29 18:32:15 73423 [Note] Server socket created on IP: '::'.
2021-03-29 18:32:15 73423 [ERROR] Fatal error: Can't open and lock privilege tables: Table 'mysql.user' doesn't exist
210329 18:32:16 mysqld_safe mysqld from pid file /usr/local/var/mysql/doishinichirounoMacBook-Pro.local.pid ended
210329 18:32:26 mysqld_safe Logging to '/usr/local/var/mysql/doishinichirounoMacBook-Pro.local.err'.
210329 18:32:26 mysqld_safe Starting mysqld daemon with databases from /usr/local/var/mysql
2021-03-29 18:32:26 0 [Warning] TIMESTAMP with implicit DEFAULT value is deprecated. Please use --explicit_defaults_for_timestamp server option (see documentation for more details).
2021-03-29 18:32:26 0 [Note] --secure-file-priv is set to NULL. Operations related to importing and exporting data are disabled
2021-03-29 18:32:26 0 [Note] /usr/local/opt/mysql@5.6/bin/mysqld (mysqld 5.6.51) starting as process 73504 ...
2021-03-29 18:32:26 73504 [Warning] Setting lower_case_table_names=2 because file system for /usr/local/var/mysql/ is case insensitive
2021-03-29 18:32:26 73504 [Note] Plugin 'FEDERATED' is disabled.
/usr/local/opt/mysql@5.6/bin/mysqld: Table 'mysql.plugin' doesn't exist
2021-03-29 18:32:26 73504 [ERROR] Can't open the mysql.plugin table. Please run mysql_upgrade to create it.

補足情報（FW/ツールのバージョンなど）

ご教授よろしくお願い致します。

mysql5.6、、

Answer 1

qita記事
上記の記事を参考に改めて、mysqlをインストールし直すことで上記のエラーは解消できました。

Answer 2

Table 'mysql.user' 　というのが違和感あります。
config/database.yml　を（ユーザ名とパスワードは***にして）載せてください

Comments

[attakrui]

メッセージありがとうございます！下記の内容になります
config/database.yml

[winterboum]

database.ymlはmysqlでなくsqliteになってますね。
Gemfileでは何をbundleしてますか？

[attakrui]

先程は、別のファイルを記述してしまいました。
大変申し訳ありません。
改めて記述します
config/database.yml

# MySQL. Versions 5.5.8 and up are supported.
#
# Install the MySQL driver
# gem install mysql2
#
# Ensure the MySQL gem is defined in your Gemfile
# gem 'mysql2'
#
# And be sure to use new-style password hashing:
# https://dev.mysql.com/doc/refman/5.7/en/password-hashing.html
#
default: &default
adapter: mysql2
encoding: utf8mb4
pool: <%= ENV.fetch("RAILS_MAX_THREADS") { 5 } %>
username: ***
password:
host: localhost

development:
<<: *default
database: simple_calender_app_development

# Warning: The database defined as "test" will be erased and
# re-generated from your development database when you run "rake".
# Do not set this db to the same as development or production.
test:
<<: *default
database: simple_calender_app_test

# As with config/credentials.yml, you never want to store sensitive information,
# like your database password, in your source code. If your source code is
# ever seen by anyone, they now have access to your database.
#
# Instead, provide the password as a unix environment variable when you boot
# the app. Read https://guides.rubyonrails.org/configuring.html#configuring-a-database
# for a full rundown on how to provide these environment variables in a
# production deployment.
#
# On Heroku and other platform providers, you may have a full connection URL
# available as an environment variable. For example:
#
# DATABASE_URL="mysql2://myuser:mypass@localhost/somedatabase"
#
# You can use this database configuration with:
#
# production:
# url: <%= ENV['DATABASE_URL'] %>
#
production:
<<: *default
database: simple_calender_app_production
username: ***
password: ***