Server quit without updating PID file when trying to start MySQL server?

So I created my .bash_profile, opened it in a text editor and added:

export PATH=$  PATH:/usr/local/mysql/bin 

and then I saved it. Next, I tried running

sudo /usr/local/mysql/support-files/mysql.server start 

was told to enter my password (so I did), and then terminal said

Starting MySQL  

and then it kept printing dots until it said:

ERROR! The server quit without updating PID file (/usr/local/mysql/data/ 

The error logs look like:

2021-01-25T20:50:49.707062Z 0 [System] [MY-010116] [Server] /usr/local/mysql/bin/mysqld (mysqld 8.0.23) starting as process 15092 2021-01-25T20:50:49.710232Z 0 [Warning] [MY-010159] [Server] Setting lower_case_table_names=2 because file system for /usr/local/mysql/data/ is case insensitive 2021-01-25T20:50:49.834599Z 1 [System] [MY-013576] [InnoDB] InnoDB initialization has started. 2021-01-25T20:50:49.943719Z 1 [System] [MY-013577] [InnoDB] InnoDB initialization has ended. 2021-01-25T20:50:50.037810Z 0 [System] [MY-011323] [Server] X Plugin ready for connections. Bind-address: '::' port: 33060, socket: /tmp/mysqlx.sock 2021-01-25T20:50:50.125494Z 0 [Warning] [MY-010068] [Server] CA certificate ca.pem is self signed. 2021-01-25T20:50:50.126128Z 0 [System] [MY-013602] [Server] Channel mysql_main configured to support TLS. Encrypted connections are now supported for this channel. 2021-01-25T20:50:50.151069Z 0 [System] [MY-010931] [Server] /usr/local/mysql/bin/mysqld: ready for connections. Version: '8.0.23'  socket: '/tmp/mysql.sock'  port: 3306  MySQL Community Server - GPL. ~ ~ ~ ~ ~ (END) 

How do I fix this?