Debug message

location /api/ {
    add_header X-Debug-Message $destination always;
}

Proxy by request method

map $request_method $destination {
    default     service-a:80;
    POST        service-b:8000;
    PUT         service-b:8000;
    PATCH       service-b:8000;
    DELETE      service-b:8000;
}

server {
    ...
    location /api/ {
        proxy_pass http://$destination;
    }
}