Yes this is a known issue.They removed access to root dir

First identify your mongod.conf.It should be under /usr/local
If you see the contents of config file it will show your mongo.log path
If it is failing due to dbpath issue simply create a directory under your home directory and update your config file
Restart the service.It should start mongod on default port 27017

You can start your own mongod on another port say 28000 by below command
mongod --port 28000 --dbpath your_dbpath --logpath your_logpath --fork
Give valid full path for dbpath and logpath where the owner of mongod can write

Check mongodb documentation and this link

https://saiankit30.medium.com/setting-up-mongodb-on-macos-catalina-common-errors-and-their-solutions-72fd66fb8a86