How do I remove /web from the URL?
You should have your host point directly to the "web" directory instead of your project root. I've run into this issue on webfaction hosting and my solution (actually my co-worker's) was to have 2 "apps." The first app is not web accessible and this is where my drupal-composer/drupal-project's root is. Then I create a second app that is web accessible, e.g. domain.com and is a symlink to the first apps /web directory. Maybe you can use this same approach.