So far as I can tell this default container works fine:

root $ 
root $ docker container list
CONTAINER ID        IMAGE                       COMMAND                  CREATED             STATUS                  PORTS                               NAMES
7b119ef62a85        mysql/mysql-server:latest   "/entrypoint.sh mysq…"   17 hours ago        Up 17 hours (healthy)   0.0.0.0:3306->3306/tcp, 33060/tcp   mysql
root $ 
root $ mysql -h127.0.0.1:33060 -p -uroot
Enter password: 
ERROR 2005 (HY000): Unknown MySQL server host '127.0.0.1:33060' (22)
root $ 
root $ mysql -h127.0.0.1 -p -uroot
Enter password: 
ERROR 1130 (HY000): Host '172.17.0.1' is not allowed to connect to this MySQL server
root $ 
root $ docker exec -ti --user root mysql bash
bash-4.2# 
bash-4.2# mysql -u root -p
Enter password: 
Welcome to the MySQL monitor.  Commands end with ; or \g.
Your MySQL connection id is 2021
Server version: 8.0.21 MySQL Community Server - GPL

Copyright (c) 2000, 2020, Oracle and/or its affiliates. All rights reserved.

Oracle is a registered trademark of Oracle Corporation and/or its
affiliates. Other names may be trademarks of their respective
owners.

Type 'help;' or '\h' for help. Type '\c' to clear the current input statement.

mysql> 
mysql> exit
Bye
bash-4.2# 
bash-4.2# exit
exit
root $ 

How do I connect to the database directly from the host? Using:

Products Included in the Container

A number of MySQL products are included in the Docker container you created with the MySQL Server Docker image:

MySQL Server and other MySQL Programs including the mysql client,mysqladmin, mysqldump, and so on. See the MySQL Reference

Manual for documentation of the products.

although a simple console prompt acquired through bash from the host would be sufficient.

Rather than Connecting to MySQL Server from within the Container or Container Shell Access

I'm looking for access from the host.

from the container:

mysql> 
mysql> select user,host from mysql.user;
+------------------+-----------+
| user             | host      |
+------------------+-----------+
| healthchecker    | localhost |
| mysql.infoschema | localhost |
| mysql.session    | localhost |
| mysql.sys        | localhost |
| root             | localhost |
+------------------+-----------+
5 rows in set (0.00 sec)

mysql> 

and:

bash-4.2# 
bash-4.2#  mysqld --verbose --help | grep bind-address
  --bind-address=name IP address(es) to bind to. Syntax: address[,address]...,
  --mysqlx-bind-address[=name] 
bind-address                                                 *
mysqlx-bind-address                                          *
bash-4.2# 

I updated the privileges as:

mysql> 
mysql> CREATE USER 'user'@'%' IDENTIFIED BY 'password';
Query OK, 0 rows affected (0.40 sec)

mysql> 
mysql> GRANT ALL PRIVILEGES ON *.* TO 'user'@'%' WITH GRANT OPTION;
Query OK, 0 rows affected (0.21 sec)

mysql> 
mysql> FLUSH PRIVILEGES;
Query OK, 0 rows affected (0.06 sec)

mysql> 
mysql> SELECT host, user FROM mysql.user;
+-----------+------------------+
| host      | user             |
+-----------+------------------+
| %         | user             |
| localhost | healthchecker    |
| localhost | mysql.infoschema |
| localhost | mysql.session    |
| localhost | mysql.sys        |
| localhost | root             |
+-----------+------------------+
6 rows in set (0.00 sec)

mysql> 
mysql> exit
Bye
bash-4.2#