We use Azure Storage and Azure CDN for both Umbraco 8 and 9 using the official/recommended packages.

So we technically never emit (or generate) absolute media URLs, we always generate CDN URLs. We use GetCropUrl() to emit img srcs for example. So I can't say 100% that generating "URLs to media" work, only that generating "CDN URLs to media" works.

Everything works out of the box after configuring the Storage and CDN settings:

"Storage": {
  "AzureBlob": {
    "Media": {
      "ConnectionString": "...",
      "ContainerName": "themediacontainer",
      "Cdn": {
        "Url": "https://our-cdn-endpoint.azureedge.net/"
      }
    }
  }
},

In Startup.ConfigureServices():

        if (!_env.IsDevelopment())
        {
            // Add the Azure Blob Storage file system, ImageSharp image provider/cache and middleware for Media:
            u.AddAzureBlobMediaFileSystem()
            // Optionally add the CDN media URL provider:
            .AddCdnMediaUrlProvider(options =>
            {
                var settings = _config.GetSection("Umbraco:Storage:AzureBlob:Media:Cdn");
                options.Url = new Uri(settings.GetValue<string>("Url"));
            });
        }

The CDN endpoint is set to fetch origin media from https://site/media/, so you could say the actual media URL pattern is hard-coded into the CDN configuration.

Why configuring the CDN media URL provider is necessary I can't recall, but the emitted CDN media URL was broken somehow. It was either lacking an URL segment or containing a superfluous URL segment.

Hmm ok thanks. I'll take another look. Currently my startup looks like so:

// Add the Azure Blob Storage file system, ImageSharp image provider/cache and middleware for Media:
            .AddAzureBlobMediaFileSystem(options => {
                options.ConnectionString = Environment.GetEnvironmentVariable("UMBRACO__STORAGE__AZUREBLOB__MEDIA__CONNECTIONSTRING");
                options.ContainerName = Environment.GetEnvironmentVariable("UMBRACO__STORAGE__AZUREBLOB__MEDIA__CONTAINERNAME");
            })
            // Optionally add the CDN media URL provider:
            .AddCdnMediaUrlProvider(options =>
            {
                options.Url = new Uri(Environment.GetEnvironmentVariable("UMBRACO__STORAGE__AZUREBLOB__MEDIA__CDN__URL"));
            })

It looks like you're only missing the media segment in the CDN URL. We don't use that segment. So if you just add /media to your CDN URL it looks like it should work.

Unfortunately that doesn't work either.

In the older storage providers the cache folder used to house copies of the media when it was requested; but I'm not seeing that within my cache folder on blob storage.

The structure of my cache folder on blob storage is as follows: Umbraco > Cache > files (e.g. "445ffae" with no extension and a content type of application/octet-stream). That's quite different to what I used successfully many times in terms of older versions of the storage provider when it was pulling images back via the CDN.

Did you ever find a solution to this?