PostgreSQL, fix the `psql: error: could not connect to server` error

I had this problem: I had installed PostgreSQL in the past using Homebrew, then I think I updated its version mindlessly with brew upgrade, and I couldn’t start it again.

It used to work, but now whenever I tried to access it, I got this error:

psql: error: could not connect to server: No such file or directory
	Is the server running locally and accepting
	connections on Unix domain socket "/tmp/.s.PGSQL.5432"?

The server was running fine, as ps aux | grep postgres showed its process.

I tried various solutions, until simply reinstalling it worked fine.

I ran

brew uninstall postgresql
brew install postgresql
brew services start postgresql

and I was able to connect to the database again.