Unable to resolve dependency tree error when installing npm packages
This is not related to an HTTP proxy.
You have dependency conflict (incorrect and potentially broken dependency) as it says, so try to run the command with --force, or --legacy-peer-deps. If it doesn't take effect, the temporary solution is using prior versions of the Node.js (downgrading the Node.js version) as it causes this kind of errors to happen sometimes.
Update based on the OP's update:
As you see, it fires the following error:
No matching version found for @angular/http@^9.1.4.
Take a look at angular/http page. Note that the latest version for that deprecated package is 7.2.16 while you request an upper version (e.g., ^9.1.4)! So, try to check the project dependencies and follow the raised errors in order to solve the problem.
In addition to using the --legacy-peer-deps command line option, this can also be set more permanently as a config option:
npm config set legacy-peer-deps true