annoy bug red dot on Phone app not going away

Mmmm ... no password option ..... maybe that is something to do with your carrier ?

or maybe VoiceMail has not yet been set-up on your phone .... so no password for it.

Here's Apple support's article on VoiceMail, perhaps setting up VoiceMail,

or checking other settings may vanquish that red dot ?

Check your voicemail on iPhone – Apple Support

Seems the red dot is a notification of VoiceMail

Check Settings > Phone >

You might need to enter a VoiceMail password ..

scroll down to tap "Change VoiceMail password"

You can likely enter the correct password for VoiceMail there.

First try a Forced restart

Click here  Force restart iPhone – Apple Support (UK)

It will eventually go away

It is new with iOS16. Go to the phone app and read whatever voice message is showing there.

If you have a missed call it shows the red dot with +1 on it