nginx different routes for / and /*

I'd like to route / to a.sock and /(.*) to b.sock.

I tried

    location / {
        proxy_pass http://unix:/tmp/a.sock;
        proxy_read_timeout 30;
        proxy_connect_timeout 30;
        proxy_redirect off;
        proxy_set_header Host               $host;
        proxy_set_header X-Real-IP          $remote_addr;
        proxy_set_header X-Forwarded-For    $proxy_add_x_forwarded_for;
        proxy_set_header X-Forwarded-Proto  $scheme;
    }
    location ~ /(.*) {
        proxy_pass http://unix:/tmp/b.sock;
        proxy_read_timeout 30;
        proxy_connect_timeout 30;
        proxy_redirect off;
        proxy_set_header Host               $host;
        proxy_set_header X-Real-IP          $remote_addr;
        proxy_set_header X-Forwarded-For    $proxy_add_x_forwarded_for;
        proxy_set_header X-Forwarded-Proto  $scheme;
    }

with different ordering too.

Can this be achived with nginx, if so, how?

My take is, according to the documentation anything ending with a / assumes a wildcard after the / and the plain route without the regex takes precedence.

Essentially the backend on b.sock has a route definition of /:term or /{term} depending on which routing lib you use, but has no handler for /. You're probably thinking "so add a handler for / and call it a day". I might do that, but it's a workaround. I would like a.sock to handle /.

So again, can this be done with nginx and how?