When using the "show underlying data" context action on the dashboard, the filters saved with the visualization are not applied to the resulting discover view. As a user I would expect this action to apply all the filters which are in effect on the dashboard as well.

Steps to reproduce:

• Create a visualization with a filter pill (fieldA: 1)
• Save the visualization
• Put the visualization on a dashboard
• The visualization will only show data matching fieldA: 1
• Use the "show underlying data" action
• Discover should have fieldA: 1 filter pill

This would probably require us to extend the embeddable output with the local filters - at least Visualize visualization types and Lens can provide this information.

cc @streamich

Related: same for saved search #82615