Hey there remisbowman,
Thanks for using Apple Support Communities!
We understand you are seeing some issues when you turn your iPhone to silent, it also mutes your Apple Watch. We are happy to go over some information and provide some guidance.
What you are seeing is expected behavior if you have the notification settings on your Apple Watch set to mirror your iPhone. You can manage these settings by going to the Watch app on your iPhone. Take a look at the steps listed in this resource that goes over setting your notification settings:
Notifications on your Apple Watch
Specifically the section titled "Customize your notification settings".
We hope this helps.
Best Regards.