Microsoft
Microsoft
I am not familiar with LAPS-E. Based on your description though there are significant architectural differences between this new Windows LAPS feature and LAPS-E. It sounds like LAPS-E is designed around extra servers which are targeted by the client-installed MSI binaries, and I am guessing the passwords end up in a SQL server db or similar. There are advantages to that approach - you can very tightly control who can access those passwords, but now you also have to be concerned with uptime of those extra servers, which is probably where that primary\secondary failover relationship comes from. Again, nothing wrong with that approach.
For Windows LAPS though, I wanted a clean, Windows-integrated feature that works with one of the most reliable and redundant stores out there, ie Active Directory, with no further infrastructure required. Or put another way, I wanted the new design to not have any larger dependency requirement than what "legacy LAPS" had, and we can pretty much assume that any customer interested in LAPS also has a deployed and working Active Directory environment. Sure, there could be pros\cons to this approach as well - but I felt on balance this was the way to go.
So I don't know the full answer to your question, but it seems likely that if Windows LAPS meets your requirements you would be able to transition away from all of that extra LAPS-E infrastructure.