The documentation is purposefully deceiving. It makes you believe, in good faith, that disabling telemetry is per project when in reality it is per machine.

I just tried it myself on a brand new Next project:

    $ npx create-next-app@latest
    
    ...

    $ npx next telemetry disable
    Next.js' telemetry collection is already disabled.
    Status: Disabled
    You have opted-out of Next.js' anonymous telemetry program.
    No data will be collected from your machine.
    Learn more: https://nextjs.org/telemetry

Note the part that says "from your machine".

An issue was crated about it but they just closed without responding: https://github.com/vercel/next.js/issues/31360