试试下面这样的东西。它利用了Cosmos DB.NET SDKV3。

            CosmosClient client = new CosmosClient("cosmos-db-connection-string");
            using (FeedIterator<DatabaseProperties> iterator = client.GetDatabaseQueryIterator<DatabaseProperties>())
            {
                while (iterator.HasMoreResults)
                {
                    foreach (DatabaseProperties db in await iterator.ReadNextAsync())
                    {
                        Console.WriteLine(db.Id);
                    }
                }
            }

您可以在这里找到更多示例:https://github.com/azure/azure-cosmos-dotnet-v3/tree/master/microsoft.azure.cosmos.samples。