I was unable to find a listing of SQL database backups in the Azure Portal. Eventually I found this helpful DMV.
--AzureDatabaseBackups.sql
SELECT @@SERVERNAME server_name,
DB_NAME() database_name,
backup_start_date,
backup_finish_date,
CASE backup_type
WHEN 'D' THEN 'Full'
WHEN 'I' THEN 'Differential'
WHEN 'L' THEN 'Transaction Log'
ELSE '' END backup_type
FROM sys.dm_database_backups
WHERE in_retention = 1 /* Available */
ORDER BY backup_start_date DESC;