ACOT-exclusive capital buildings don't count as upgraded capital buildings for using the 2nd city district specialization. After Superior Constructs finishes, you will no longer be able to build or change the 2nd district specialization. Also upgrades for buildings like the Autocthon Monument and Uplink Node aren't usable either.
This also applies to the Dark Pylon and Spire which generate Dark Energy and Dark Matter.

A bunch of buildings requiring an upgrade capital building just aren't usable.