Power Automate visual for Power BI not appearing when embedded in canvas app tile

Question

I created a Power BI dashboard that contains the Power Automate visual for Power BI, and this visual appears and works as expected in the dashboard itself on PBI Service. But when I embed the dashboard via the Power BI tile in a canvas app, all other dashboard visuals (slicers, a card, and a table) appear but the Power Automate visuals do not. There is no error displayed, just blank space where they should be. When the tile initially loads there's an outline where it looks like they're about to render, but then nothing happens when everything else loads.

I recreated this issue with two totally different dashboards/flows/workspaces/apps, and I'm the creator/owner of the dashboard, flow, and app so I don't think it's a permissions issue. I'm getting the same issue with the AllowNewAPI property of the Power BI tile in the app set to either true or false.