Server quit without updating PID file when trying to start MySQL server?
I think the problem might be the PID file
There are two I can see
One in the directory
/usr/local/mysql/data/mysqld.local.pid

and one in the error message
/usr/local/mysql/data/Nicks-MacBook-Pro.local.pid

Please delete those two pid files if they still exist.
Then, start mysql and let’s us know what happens.
I have suggested this twice in the past, 4 years ago and 6 years ago
Before doing so, check to make mysqld is not running.
ps -ef | grep -v grep | grep mysqld

If you see mysqld still running, kill the process, then delete the pid files and retry starting mysql.
UPDATE 2021-01-29 15:56 EST
As it turns out, there were two installations of MySQL involved on the Mac as was learned in the Chat Session.
One installation was done as a dmg install; the other was a homebrew installation.
Once it was discovered that homebrew was competing with the dmg for the PID file, it was decided to stop using the dmg version and use the homebrew version via brew services approach.
The two installs were butting heads, having different PID files.