Hi, @Franz Thanks for the ask and for using the Microsoft Q&A platform.
For MySql, We have an on-demand backup which is in our roadmap, we don't have any ETA yet.
On the Postgres SQL, there is no offer as such however you can always do a logical backup for instance with pg_dump
For Azure SQL DB, there are no plans to allow invoking a database backup on demand. However, the built-in backup and restore mechanisms already allow a precise point-in-time restore within the specified retention period. you mentioned 7 days of retention – it should be noted that 7 days is not the start time for the first backup.
Please let me know if this information is helpful
Regards
Geetha