That new sprocket is AM not Stihl and may be part of your issues. Ir is also not likely to last near as long as an OEM.
Before you invest in a new chain for that bar you should check the bar groove width for excessive wear with a feeler gauge. If the bar groove is worn excessively the chain will flop from side to side causing issues. A new .050" bar should measure about .053" +/- . I have one that is worn to about .058" and is noticeably too loose.
The original worn sprocket is Stihl, and I mainly got the AM replacements just to see if they would help with the slack (they were like 3 for $10). I've not run them at all yet, since the chain is still way too loose to even try.
I'm measuring no worse than .054, so probably not too bad.
The bar I have has apparently been discontinued by Stihl, but I hope to have a little time tomorrow to check a couple of local retailers here to see what they have in stock. Looks like the .325 bar Stihl specifies for this saw is only about $40, so if they don't have a 3/8 chain to fit the old bar I have, I might just go ahead and get a new sprocket, bar, and chain. I usually just order everything, but in this case I'll try to buy local so I can return/swap easily if needed.