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Is there an instruction how to bootstrap  pulumi on a new machine but let it access an existing stack with standard backend
I'm struggling with  "If you have not created a project yet, use `pulumi new`"

yeah you will login to the account with the stack and it will be accessible to you

<https://www.pulumi.com/docs/cli/commands/pulumi_login/>
<https://www.pulumi.com/docs/concepts/state/>

you might find `pulumi login` command or `PULUMI_BACKEND_URL` environment variable useful

Getting access to the stack and stack state is done via `pulumi login`, assuming that you didn’t use local/file state on the first machine. Access to the project files is separate; you’d typically use a Git repo and then clone that to the second machine.