FPM takes request URI from the SCRIPT_NAME. I guess this is more a documentation issue (more description in docs maybe) / feature request so I will change this to feature request as we can't just change it at this stage anyway.

I assume that you really want to be able to log path info, right?

Yes, you are right.

And honestly, I don't think that there is a documentation issue.
As I can see, access.format has dedicated placeholder "%f" for script_filename and it seems strange to use "%r" just for script_name (without full path to that script). It seems like "%r" intended to contain certainly request URI (or path info).

What I meant that we should update documentation to state that "%r" is for SCRIPT_NAME rather than for REQUEST_URI fcgi env. We cannot just change the value as it could potentially break some scripts that already depend on it being a SCRIPT_NAME. The thing is that internally script name is taken as request uri so I don't think REQUEST_URI is used for anything but might have missed something.

In your case it doesn't really matter that much because if we just changed it to REQUEST_URI than it would contain a query so I guess it wouldn't help you. I guess specific flag for path info might help as it might not be always reliable to get it from env (at least the logic around that doesn't seem that straight forward as there are some hacks around Apache). You might actually give it a try and see if "%{PATH_INFO}e" or "%{ORIG_PATH_INFO}e" works for you?

"%{PATH_INFO}e" produces empty string, "%{ORIG_PATH_INFO}e" produces "-".

I have the following nginx configuration:

server {
    ...
    location / {
        try_files $uri /index.php$is_args$args;
    }

    location ~ ^/index\.php(/|$) {
        fastcgi_pass unix:/run/php/php8.1-fpm.sock;
        fastcgi_split_path_info ^(.+\.php)(/.*)$;

        include fastcgi.conf;
        internal;
    }
    ...
}

Another one place where the same problem takes place — status page.
There "request URI" also shows the SCRIPT_NAME (with query string) instead of REQUEST_URI (see https://bugs.php.net/bug.php?id=72319).