Export Power BI report into CSV

Anonymous Publish to web has many limitations, one of which is exporting information from visuals. You will need to use a secure embedding solution instead.

• Reports using row-level security.
• Reports using any Live Connection data source, including Analysis Services Tabular hosted on-premises, Analysis Services Multidimensional, and Azure Analysis Services.
• Reports using a shared dataset that is stored in a different workspace from the report.
• Shared and certified datasets.
• Reports shared to you directly or through an app.
• Reports in a workspace in which you aren't an edit member.
• "R" and Python visuals aren't currently supported in Publish to web reports.
• Exporting data from visuals in a report that has been published to the web.
• Q&A for Power BI visuals.
• Reports containing report-level DAX measures.
• Single sign-on data query models.
• Secure confidential or proprietary information.
• The automatic authentication capability provided with the Embed option doesn't work with the Power BI JavaScript API. For the Power BI JavaScript API, use the user owns data approach to embedding.
• Admins can block public internet access, as described in Private links for accessing Power BI. In that case, the Publish to Web option is grayed out for your tenant in the Power BI admin portal.

Publish to web from Power BI - Power BI | Microsoft Docs