Azure SQL Database Restore after Server Failure - Where are the Backups?

I think the key to understanding that sentence is what I have marked in bold:

Restore a database to another geographical region. This allows you to recover from a geographic disaster when you cannot access your server and database. It creates a new database in any existing server anywhere in the world.

See the documentation on Geo restore:

Geo-restore is the default recovery option when your database is unavailable because of an incident in the region where the database is hosted. If a large-scale incident in a region results in unavailability of your database application, you can restore a database from the geo-replicated backups to a server in any other region. There is a delay between when a differential backup is taken and when it is geo-replicated to an Azure blob in a different region. This delay can be up to an hour, so, if a disaster occurs, there can be up to one hour data loss.

The difference between this and a regular restore is that there is a bigger latency and possibility of data loss. You also can't do a point in time restore.

So when you restore the backup from an existing database through the azure portal you have access to the backups on that same location.

Microsoft is replicating those backups to azure blobs in different regions in case some serious incident happens in a region.

In order to restore you would add a new database in your portal and select "backup" as a source:

To geo-restore a database during its retention period using the Azure portal, open the SQL Databases page and then click Add. In the Select source text box, select Backup. Specify the backup from which to perform the recovery in the region and on the server of your choice.

So in case your entire database and data center is gone, you have the option to create a new database in another data center, and you can use the latest geographically replicated backup (not the latest backup) as a source.

In the event the server my database is sitting on fails how would I be able to access the most recent backup to restore it to another server?

Your option is following unless you had Geo-Replicaiton configured.

A new database on any logical server in any region recovered to the point of the most recent daily backups in geo-replicated blob storage (RA-GRS).

I have 3 logical server. 2 in the same location and one in a different location.

I have one database named original in server swwazuretest.

Now I am simulating that server swwazuretest is destroyed by deleting it.

I can restore in either one of my 2 other remaining logical server. One in the same data center (location) and other one in another location. After you click New database, from the drop down of select source chose backup. You will see the list of available backup on the right side.

Once you restore in other location you might lose data. SLA is described in this document.

Overview of business continuity with Azure SQL Database