>> I see no way to set the same project name both for
>> non-file and file buffers.
>
> Please try the patch below. It might have non-negligible effect on
> performance though. Please try and report back.
>
> diff --git a/lisp/progmodes/project.el b/lisp/progmodes/project.el
> index 7c51778d5d4..1494665d565 100644
> --- a/lisp/progmodes/project.el
> +++ b/lisp/progmodes/project.el
> @@ -816,8 +816,8 @@ project-buffers
>          (push buf bufs)))
>      (nreverse bufs)))
>
> -(cl-defmethod project-name ((_project (head vc)))
> -  (or project-vc-name
> +(cl-defmethod project-name ((project (head vc)))
> +  (or (project--value-in-dir 'project-vc-name (project-root project))
>        (cl-call-next-method)))

Thanks, I confirm this uses project-vc-name from dir-locals in non-file buffers.

>> The standard solution is just to use e.g.:
>> ;;;###autoload(put 'compilation-directory 'safe-local-variable 'stringp)
>
> Huh, so the attribute :safe only makes proper sense for preloaded packages
> and autoloaded defcustom forms (which are discouraged anyway).
>
> Do you want to write a patch for all those vars in project.el? It will
> probably make sense to push it to emacs-29.

With this patch the problem is solved.  I can push it to emacs-29.