When you try to create an EUM application for Synthetic Monitoring, you receive a "You do not have a license for Synthetic Monitoring" error.
In reviewing the license, you only see the Browser and Mobile Licenses. The Synthetic License does not appear, because it has not been synced.
The "You do not have a license for Synthetic Monitoring" error indicates that the controller has not synced with the EUM Cloud for the Synthetic Licenses. The controller will need to be force-synced to the EUM cloud.
Since the EUM App Creation wizard is throwing the error "You Do Not Have License for Synthetic Monitoring" you know you can't create the app from the EUM App Creation Wizard. Instead, go to an existing application in APM and enable EUM from there. This action will force the controller to sync to the EUM cloud.
You will be able to use that application for synthetic EUM. Alternatively, once the sync resumes and you can use the EUM App Creation wizard as expected, you can return to it and disable EUM for that application.
Go to an existing application in your APM
Click Configuration in the sidebar
Under Instrumentation, click the End User Monitoring tab
Click the Enable End User Monitoring checkbox
Click the Save button
When completed, the controller will force sync back to the EUM Cloud. You will also be able to create applications for Synthetic from the EUM App Creation Wizard.
After this is done, you can either start using this EUM application for Synthetic, or you can create a new one from the EUM App Creation Wizard.
If you don't want to use the app you just configured for Synthetic, return to its configuration panel following the above steps, but un-check its EUM checkbox.