Hi @Łukasz Zbińkowski (UZ) ,
Welcome to Microsoft Q&A forum and thanks for using Azure services.
As I understand from the question, you want to know about Azure SQL Database monitoring having configured LTR weekly.
In Azure SQL Database, the first full backup is scheduled immediately after a new database is created or restored. This backup usually finishes within 30 minutes, but it can take longer when the database is large. For example, the initial backup can take longer on a restored database or a database copy, which would typically be larger than a new database.
After the first full backup, all further backups are scheduled and managed automatically. The exact timing of all database backups is determined by the SQL Database service as it balances the overall system workload. You can't change the schedule of backup jobs or disable them.
All backups are shown for the in the SQL Server as below:
Use following T-SQL command to query sys.dm_database_backups and view list of all active backups for this database:
Select * from sys.dm_database_backups
ORDER BY backup_finish_date DESC
References: Azure SQL DB Backup History - View backups of your Azure SQL Database
Long-term backup retention (LTR) leverages the full database backups that are automatically created to enable point in time restore (PITR). If an LTR policy is configured, these backups are copied to different blobs for long-term storage. The copy is a background job that has no performance impact on the database workload. The LTR policy for each database in SQL Database can also specify how frequently the LTR backups are created.
Note:
The timing of individual LTR backups is controlled by Azure. You cannot manually create an LTR backup or control the timing of the backup creation. After configuring an LTR policy, it may take up to 7 days before the first LTR backup will show up on the list of available backups.
Refer: Long-term retention - Azure SQL Database
If you want to see Backups in Azure Backups Center, you may share you idea in Azure SQL Database Feedback Channel to get this feature added. Concerned team will work on the feedbacks depending on the importance and up-votes.
Hope this helps. Let us know if further queries. Thank you.