what is the bell with wave icon in control center on Apple Watch SE? It is grayed out so I can't activate it. I want all sound turned off and activated the regular bell icon but I still get a ding when a text comes in.

That icon would work if you were wearing AirPods. See this link --> Use Control Center on Apple Watch - Apple Support

Are any of the text notifications you are getting coming from anyone in your favorites list? If yes, even muted, favorite contacts can still come through.

You might want to consider using Haptics as opposed to sounds on your watch. If you turn off sounds and use Haptics, you'll get a tap on your wrist, but no sound when a text message arrives. I don't use sounds at all on my Apple Watch.

Don't have anyone in your favorites list, is the only way to completely silence everyone. But then you might miss something important. This is why I use Haptics instead of sounds on my Apple Watch. I used to miss dings, but I rarely if ever, miss a tap on my wrist. And people around me are happier not having to hear my wrist ding.

Thank you for taking the time to respond. I really appreciate it. I am fine with just the vibration on my wrist. I really don’t want to have any of the dinging or sounds, that’s why I wondered why it was still doing it, even though I had tapped on the bell to silence that sound.

You're welcome.