For questions on where to find this when you're using Neo4j Desktop, the good news is there should be a way to open up the directory via Desktop itself.
Find the database entry whose home directory you want to open, and you should see a ... right after the Open button. Clicking on that should open up a dropdown, and one of the entries is Open folder which expands the dropdown, and the top entry there is DBMS. This will open the home directory for this dbms instance.
If you're looking for how to get there in your terminal, from the ... dropdown there should be a Terminal option, which should open your terminal to the dbms's home directory.