No, if you already have Bold Reports for your team, you do not need to buy an additional license for deploying your applications to Azure App service. You should register the license token on initial startup of your application as explained in the following documentation.
Can the Syncfusion community license be used with Bold Reports
Can the Report Viewer component be accessed from Bold Reports using Syncfusion community license
Can the Report Designer component be accessed from Bold Reports using Syncfusion community license
Can the Report Designer component be used from Bold Reports using Syncfusion license
Is Report Designer included with Report Viewer SDK to create Reports