So it was pretty bizarre. Basically as soon as I punched the "Dial" button it would show the "modal dialog" of the number being dialed and then immediately hang

So it was pretty bizarre. Basically as soon as I punched the "Dial" button it would show the "modal dialog" of the number being dialed and then immediately hang itself up. It happened pretty inconsistently, but I managed to make it happen against another person - who also had a Pixel phone so I don't think it was related to the "Do Not Disturb" mode. I'd assume DND would at least put you through to voicemail though.