May I know what’s your roles in the original workspace and the target workspace? To publish a report, you must be Contributor, Member or Admin in the workspace so that you will have Edit permissions to allow you to do operations like publish.
Is this issue happening in all target workspaces or just some specific workspace?
What’s the type of your original workspace? Is it a My workspace, Classic workspace or New workspace?
What’s your data source of the live connected dataset? Did this dataset enable cloud RLS?
There are some Consideration and limitations on datasets across workspaces. For more details about using datasets across workspaces, please refer to the official document.
As an app publisher you have to make sure that your audience has access to datasets outside of the workspace. Otherwise, users will encounter issues when interacting with your app: reports won’t open without dataset access, and dashboard tiles will show as locked. Also, users won’t be able to open the app if the first item in its navigation is a report without access to the dataset.
Building a report on top of a dataset in a different workspace requires the new workspace experience at both ends: The report needs to be in a new workspace experience and the dataset needs to be in a new workspace experience. You can only copy reports in a new workspace experience to another new workspace experience, and not to classic workspaces or to My Workspace.
In a classic workspace, the dataset discovery experience only shows the datasets in that workspace.
By design, “Publish to web” doesn’t work for a report based on a shared dataset.
If two people are members of a workspace that is accessing a shared dataset, it's possible that only one of them can see the related dataset in the workspace. Only people with at least Read access to the dataset can see the shared dataset.