Why would Soris Arenim's house key be in the evidence chest at Anvil dungeons?

You can start to look guilty right now
You have stolen it once a very long time ago, then you was arrested for something, the guards also take your stolen goods if you pay the fine.
Much later you searched the chest and found it.

Ha. It's the most likely answer, of course. But I'm so sure I've never been arrested in Anvil. In fact, I haven't spent a great deal of time there at all, despite my 70+ hours of game time so far.

Its possible - and extremely annoying - that you were arrested on the road or an inn somewhere, and taken to the Anvil prison, even if you were nowhere near Anvil.

I was on the green road just north of Leyawiin once, got arrested, and was taken to the Cheydinhal castle.