How to turn this switched duplex receptacle into half-hot
The two white wires are "common coming in" and "common going out". Leave them alone.

Your red group might be "power in" and "power out to switch", with the separate red being "switched power returning from switch". Or the red group might be switched, or something entirely different.

I'd suggest that you turn the breakers back on, and see what wires are switched. That will tell you if the red nut group is good to use.

If the red nut group is switched also, then you'll have to take power from the black nut group for your unswitched half.