That's a good start!
I'd say that's an allowable amount of float.
It wobbles a little more than a bit, but not as much as a lot
Kidding, I'll get a quick video of it later when I put the chain back on.
Is your sprocket held on by a big nut or a retaining plate secured with small bolts? Yes, float is normal, no spec I know of. The retaining plates do wear though.
It's the old sort with the retaining plate and two bolts, with a brand spankin new plate from Italy. Or, wherever it came from off ebay.