Q: IOS 10.0.2 not showing up on iPhone 5s

Since you're on a newer iOS verison (10.1) you will not see the 10.0.2 update, despite deleting the iOS Beta Software Profile

You need to update manually with an iOS 10.0.2 IPSW (just Google Search for one, as I cannot link one here)

For a Windows PC, iTunes > iPhone > Shift + Check for Update > (the file you just downloaded)

Depending on your internet connection and speed, the IPSW file might take some time to download

Hey, here again with a followup message just wondering if this fixed your issue or can I further assist you