Nginx configuration skipping if statement in parent location block

I have the following setup:

location @public {
    auth_basic off;
}
location @webdav {
    proxy_set_header Host $host;
    proxy_pass http://localhost:8080;
}
location / {
    # WebDAV server
    if ($request_method != GET) {
        error_page 418 = @webdav;
        return 418;
    }
    gzip on;
    fancyindex on;

    location ~ /(public|\.well-known)/ {
        if ($remote_user = "") {
            error_page 418 = @public;
            return 418;
        }
    }
    location = /robots.txt {
        add_header Content-Type text/plain;
        return 200 "User-agent: *\nDisallow: /\n";
    }
}

I want to redirect every non-GET request to my internal WebDAV handler written in Go. the /public folder should be accessible without basic auth, unlike the rest of the filesystem.

However, for nested location blocks, my parent if statement seems to be ignored. Attempting any non-GET request on /public results in 505, and on /robots.txt returns my configured text. However, this is not the case with gzip or fancyindex, as both /public and robots.txt are gzipped and fancy indexed.