The following issues might be seen when trying to publish the segment created on a Virtual Report Suite (VRS):
Virtual Report Suite is not supported for publishing segments to the Experience Cloud.
VRS cannot have their own data source and is not used for data collection. There is no Experience Cloud ID association for a VRS.
Unless there is an Experience Cloud ID association, the checkbox to publish the segment to the Experience Cloud will not be visible in the UI.
It is recommended to use the parent report suite to create the segment that has to be published to the Experience Cloud.