Updates on this have been slowly trickling out and the best I can discern is you will be able to still install apps from stores like F-Droid, but you have to go through a manual "advanced flow" which will most likely make you wait 24 hours before installing it and make you go through other hoops.

In short, google has referred to this as "increased user friction" to try and deter people from doing this. Essentially not making it impossible; just really frustrating for users so they get sick of the process and just install verified apps through them.

The only way I know around this is to install a custom rom like GrapheneOS or Lineage OS since this change targets Because the policy targets the Google Mobile Services (GMS) framework rather than the foundational Android Open Source Project (AOSP).