Hello Smcyork,
Welcome to Apple Support Communities, thanks for joining. Based on your post, the Apple Watch Series 6 displays the green phone icon after ending a call. We'll do our best to assist with this.
It sounds like you've taken some good troubleshooting steps for this, nice work. If they didn't solve this, then we'd want to confirm where you see the phone icon. If this happens in Control Center, then this is expected behavior, since that displays that the Apple Watch is connected successfully to your iPhone.
If that's not the case, the only other suggestion we would have is to sign out of iCloud on your paired iPhone and then sign back in: Sign out of iCloud on your iPhone, iPad, iPod touch, Apple TV, or Mac under section, 'Sign out on your Apple Watch'.
Should it continue, let us know if you're seeing the green icon in Control Center or on the Home Screen of your Apple Watch.
Wishing you the best, take care!