@Gokhan Varol Welcome to Microsoft Q&A forums and thank you for your interest in Azure services.
The time taken for scaling will vary depending on the configuration and volume of data.
For scaling General Purpose to Business Critical and vice versa, 90% of operations finish in 2.5 hours + time to seed all databases at 220 GB/hour.
These scenarios are documented in detail here
The database is online and available during the scaling operation but there is a short downtime up to 10 seconds because of the failover to the new instance. You can add a retry logic to your application to handle this scenario.
More details are here
Please let us know if you have any further questions.
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