If I said to you describe what you think post-punk sounds like I bet pretty much that the description would be similar to the music True Faith have delivered on their debut (mini?) album As Much Nothing As Possible. Slow brooding bass riffs with a nod to Peter Hook supplemented by bursts of atmospheric synths complete with gloomy words and dark vocals. Er yeah, that about encapsulates an answer.
However, rather than becoming a carbon copy True Faith supplement those sounds with contemporary electronica giving a fresh perspective to a worn well “genre” blending those goth, coldwave and synthpop influences to great effect. This is most ably demonstrated on the sublime closing track Blame. Aside from being ripe for a remix (or three!) thanks to the lovely synths, it also ticks all those boxes in your description and then some more.