I have a twelve speed Shimano derailleur and I now notice when I freewheel the chain goes very slack at the top. Gets a big bow in it. Droops down. Not every time but mostly.

Then slowly - not always - it will tighten up again.

Something wrong with that jointed arm down there I guess. But what? I've sprayed it with WD40 and it seems to move freely enough. The gear cluster seems to move easily enough.

Is there an adjustment I should look at or do I need to replace something or is set up wrong somehow? Chain too long?

Most likely you have a freewheel rear hub. ANd the freewheel isn't spinning as easily as it should. Do a net or website search for "flush a freewheel" or *service a freewheel" or "lube a freewheel", try those techniques and report back.

Remove the rear wheel. See if the freewheel spins freely in a counter-clockwise direction. If not, squirt lots and lots of WD-40 into the gap between the FW body (the part that spins) and the central, non-moving part. Spin the FW to distribute the WD-40 and see if the mechanism frees up. After the WD-40 drains out thoroughly, drip light machine oil (3-in-One, for example) into the gap and rotate the FW. If none of this helps, consider a new FW.