If you are rebooked by the system, doesn't it put you in the same cabin? I ask because on the same leg of an itinerary in paid F I rebooked multiple times (some by the system and twice by me). When looking at rebook options on the app and online, I was shown options in both First and also other cabins - in each case, a warning was displayed that if I accept a downgrade in cabins to rebook, no compensation is due or provided.
Each time the system rebooked me, it was to a flight (not always the next option) where I was in F.

I made assumptions based on this anecdotal experience, but if it will rebook in lower classes, I'll need to pay much more attention moving forward (during IROPS).