"Special Type" DDs starting with Fubuki were used for fleet service only, at least in the first years.
Later, at least the Fubukis were used as convoy escorts, some later DDs as well.
The division structure was in shambles because of high losses and DDs which could not be integrated in a coherent division because of different classes were released as escorts.
But Akizukis definitely did not belong there. These were THE high value escort ships for carriers and battleships. This was because the Akizuki was the only really AA capable IJN destroyer. Also, Akizukis were the only destroyer class still under construction in 1945 even if the program had been suspended in early 1945, but at the surrender there were a few brand new Akizukis which the chinese and the russians eagerly took over.
The Fubuki class was the watershed, the older types with the typical well deck torpedo mount and single guns were considered not first line capable anymore. But there were more of them than in SH4, also some "second rate" types a bit smaller but similar looking.
Btw, the Fubuki has the wrong torpedo mounts in SH4....