I assumed this was on a Thorn until you mentioned that you slid the dropouts. That tells me it is probably something else as I do not think any Thorns had sliding dropouts.
Thorns usually use a odd number of teeth on the hub sprocket. Other brands usually use an even number. (My Thorn Nomad Mk II has a 16 tooth cog, not the typical 17 for a Thorn bike.)
I cut a notch into one tooth on the sprocket and one notch on a tooth on the chainring, both of which have an even number of teeth. This is why.
https://www.sheldonbrown.com/chain-life.htmlIn other words, Sheldon thought that every other tooth would wear a bit more as your chain wore. And if that is the case, if you put the chain on the sprocket out of phase, that could cause more noise. And of course like you suspect, a new chain on a worn sprocket could also not run quite right.
I always make sure when I put the chain on that the tooth with a notch cut in it has a chain link with outer and not inner plates on that tooth. That goes for both chainring and sprocket.
My sprocket has had about 2000 km since the photo was taken, I have not flipped mine yet but next time I change chains, it get flipped. It does show some of that shark fin look to it.
From the photo it looks like every tooth has the same wear, but when I had the sprocket in my hand looking at it closely, I think that half the teeth had a slightly different amount of wear as half of the chain links had slightly more elongation.
