@leverem glad you made it back and posted your results. Your bar and sprocket appears to be accurate. It is to note that new bars and chains can be ruff to spin around by hand when new. They have not been run to smooth out the ruff edges. The drive links need to wear with the sprocket and bar grove to get that smooth hand pulling of the chain around the bar.
Your saw looks very clean showing the sprocket side. So I would suspect the sprocket is not worn as the picture does not show the running surface of the sprocket. Make sure you remover the sprocket every now and then and clean and lube the needle cage. Lots of YouTube on that.
Next question is what chain are you running??? Please give the specs for it. Want to make sure you have proper size chain to go with what you bought. If your chain is a "Green" then there is no real reason to get a" Yellow" bar.
Green bars have a smaller nose diameter that will help show proud the green chain safety nubs to help prevent kick back around the radius of the nose. Very tough time if you are needing to plunge / bore cut into wood. Yellow set up has none of this and a larger diameter nose that makes smoother and easier to plunge / bore cut into wood. If you are not experienced with using a chainsaw it would be suggested to stick with "Green" to protect you from yourself!!!
Stihl 362 with a 25" bar it will work, but it is at the limit of Stihls spec recommended. In our area with soft wood that is all we run, But we are mostly using a Stihl 33RSF chain. A 33RS if that all we got. Others that cut eastern hard wood can advise for your information.
Make very sure you flip over the saw and adjust the oiler all the way up to maximize oil for the bar! Keep sharp cutters and right depth gauge heights on your chain.
Patrick