I have a few ArcGIS Web Apps that would be useful to have on a Power BI Dashboard to be alongside other data. Is there any way to embed a web app into Power BI, or display a web map that's been built in AGOL? What I've read online seem to suggest that I have to rebuild my maps in Power BI; i.e. bringing in each layer and trying to get the symbology the way I want it.
Also, if the feature layers are organizational content in AGOL, and the Power BI Dashboard is in the same organization, will there be problems sharing the content on the Power BI Dashboard, or will I have to make it public?
At this time, PowerBI does not allow iFrame content, which prevents either a web app to run in powerBI or vice versa. This question caused ArcGIS for Power BI to be developed. The visual will allow you to bring in reference layers (with symbology honored if set at the layer level). More information on how this works can be found here: https://doc.arcgis.com/en/power-bi/design/add-a-reference-layer.htm
A lot of the questions you are asking about security depend on your authentication of choice in ArcGIS Enterprise / ArcGIS Online. As PowerBI and ArcGIS for PowerBI work with SAML, then there is a chance that it would use the same credentials, but I would not go so far as say it would be a SSO experience.