Reporting services 2008 reports connection to azure sql database
I assume you are talking about migrating ReportServer and ReportServerTempDB.  As per this document, Azure SQL Database is not supported.  Below are the support databases


Azure SQL Managed Instance
SQL Server 2019
SQL Server 2017
SQL Server 2016 (13.x)
SQL Server 2014 (12.x)
SQL Server 2012 (11.x)
SQL Server 2008 R2


I have done one Reporting Server migration and since we will be backup and restoring the reporting databases, the reports are migrated with it.