Can't install Ember Octane on Mac; problems with NPM and NVM

I'd like to install the most recent version of Ember on my Mac with MacOS Catalina. I actually thought I had done so a few weeks ago (this machine is only three months old), but ember -v says that Ember CLI is at version 3.9 which is 13 months old.

So I entered npm install -g ember-cli in the terminal, but I get an error:

npm ERR! Error: EACCES: permission denied, access '/usr/local/lib/node_modules'
npm ERR!  { [Error: EACCES: permission denied, access '/usr/local/lib/node_modules']
npm ERR!   stack:
npm ERR!    "Error: EACCES: permission denied, access '/usr/local/lib/node_modules'",
npm ERR!   errno: -13,
npm ERR!   code: 'EACCES',
npm ERR!   syscall: 'access',
npm ERR!   path: '/usr/local/lib/node_modules' }
npm ERR!
npm ERR! The operation was rejected by your operating system.
npm ERR! It is likely you do not have the permissions to access this file as the current user

So I did what is suggested here and tried to install nvm:

curl -o- https://raw.githubusercontent.com/nvm-sh/nvm/v0.35.3/install.sh | bash

There's some output and everything is looking finde, but when I try to verify my installation using command -v nvm, there's no output at all.

npm uninstall ember-cli gives me up to date in 0.031s.

What can I do to get Ember Octane running?