npm does not support Node.js

The correct command to update npm is npm install -g npm. At the time of this writing, that will install npm@6.14.10. (If it doesn't, try npm install -g npm@6.)

Installing npm-upgrade instead will install a CLI that updates package.json in projects. It will not update npm itself.

EDIT: The version compatibility stuff is just a warning. Based on the comment below, the ERR! cb.apply is not a function stuff is the real problem. You may have multiple versions of npm or node installed in different paths and your PATH or alias configuration is causing incompatible versions to run with each other.

EDIT (continued): If you are using nvm as a version manager, you can downgrade to a previous version, remove/reinstall the current version of Node.js, and you will have a compatible version of npm. If you are not using nvm, installing it (assuming you are on a development machine and not experiencing these issues in production) and using node and npm provided by it should also solve the issue.

EDIT PART 3: I just noticed you are running Node.js 15.5.0. That ships with npm@7 so do npm install -g npm@7. If that doesn't work, find your executable paths for node and npm. (On UNIX-like operating systems: command -v node and command -v npm.) If they are not in the same directories, that sounds like a problem and you should investigate. It will probably be easiest/best to use the npm that is in the same directory as node. You can try that out by using the full path. If that works, figure out what's wrong with your PATH or your aliases that you're using a different npm and fix that.