How to store historical reports

This needs to be handled differently if you are using direct (live) queries to a backend source compared to a conventional PBIX file where the data is Imported.

If you want to keep historcal version of your live query data you would ned to handle that in the backend DB/Cube by implemeting a reporting as at date capability. This isn't particularly easy, though temporal tables in SQL Server data sources would go a long way to providing this. Its a pretty significant undertaking however, especially for either SSAS Tabular or SSAS MD data sources and that's well beyond the scope of a forum response to answer. (there are entire books about this stuff)

If you are using conventional PBIX files with the data imported and refreshed on a schedule however it's a bit simpler. The problem with these types of PBIX files is that as well as bunch of visuals there is effectively a database strapped onto the back of it with all the data in it. So you can't just store the data, or just store the visuals, you have to store both.

So you can export the entire PBIX just before refreshing the data and keep a timestamped copy of the exported file.This will give you "versions" of the file with different data in it at the different timepoints. You could also do it the other way aorund and export the PBIX after a succesful data refresh and then import it back in using a timestamp. This is probably something you could automate with a bit of PowerShell and or the REST API.

But I can't see another obvious way of doing this other than keeping copies of the PBIX files.