>> The format is "project-branch" instead of "backend-branch".
>
> It might also be misread as a directory name. E.g. I have directories
> called "emacs" and "emacs-master" (thanks to git-worktree), and they get
> automatically assigned the corresponding project names. The new mode-line
> with your customization looks like "emacs-master-master". But that could
> just be my problem.

I had the same problem even after enabling project-mode-line,
so needed to remove the branch name from project names.

>> I'm sure that showing the backend name in all file buffers is useless
>> for most users and wastes the precious screen space.
>
> Hmm, I suppose since we're in a situation where one VCS (Git) is used 99%
> of the time, the indication might be unnecessary. But it's also a reminder
> that this mode-line item is for VC. Anyway...

The problem is that the useless word "Git" (with big G)
between the project name and the branch name is a big distraction.

>>> And if you customize 'vc-display-status' to 'with-project' but don't
>>> set project-mode-line to t, the project name won't be shown at all.
>> This is why the condition already handles this case:
>>    (and (eq vc-display-status 'with-project)
>>         (bound-and-true-p project-mode-line))
>
> What happens if mode-line-format doesn't contain project-mode-line-format,
> or has it in the wrong place? E.g. if the user (or third-party package)
> customized the mode-line.

Indeed, for such cases this option can't be used.  I believe we should
better document such situation in the docstring.

> Anyway, I've raised the questions, but I don't have strong objections to
> your patch. Perhaps consider changing the description from
>
>   (const :tag "Show project name and status" with-project)
>
> to
>
>   (const :tag "Show only status next to project name" with-project)

Currently the options are aligned and provide a nice review
what the user will see on the mode line:

 :type '(choice (const :tag "Show project name and status" with-project)
                (const :tag "Show backend and status" t)
                (const :tag "Show only backend name" nil))

So I'd rather like to describe more details in the docstring.

> and, maybe, check that project-mode-line-format precedes the vc-mode
> indicator in the current mode-line format. And otherwise keep the
> separating " ". If that makes sense to you.

Probably it should be sufficient to describe this in the docstring
like in this patch?

PS: Probably we could also add another option `no-backend'
that will show only an indicator and the branch name.
But the dangling indicator such as "-" or "*" before the branch name
doesn't look nice when there is a space that separates it
from the project name, e.g. "project -branch".