Apple Watch silent mode not preventing iPhone ringing

Theater Mode on your Watch will only silence notifications on your Watch, not on your iPhone or Mac. To silence them, you would need to set up a Focus to not disturb you and make sure that you have the Focus set to duplicate on all devices.

Your assumption was incorrect. You silenced your watch, not your iPhone. If you don't want your phone or your watch to ring, you need to silence each one individually.

In the link below are the following instructions:

Keep your Focus settings up to date across all your Apple devices

You can use the same Focus settings on all your Apple devices where you’re signed in to the same Apple Account.

Go to Settings  > Focus, then turn on Share Across Devices.

Note: Focus filters don’t get synced across devices—they’re only on the device where you set them up.

1. Go to Settings  > Focus.
2. Turn on Share Across Devices.

This link explains about everything you might want to know about Focus --> Set up a Focus on iPhone - Apple Support

You're welcome. And the suggestion Chris offered about setting up a focus, which you can share across devices is a great suggestion.

Victoria Herring wrote:

I'll get it set up = thanks for the explanation.

You're welcome. Hope you get it figured out.