That's what I have, it just allows me to charge at the same time. From what I am reading it seems that pixels have screen sharing via usbc disabled by default, google wanted everyone to use chromecast or something.
Why powered hdmi? Get a hdmi to usbc dongle and then hdmi directly into whatever monitor you desire?
Discussion
When I used to program and do stuff off my android for programming control 4/various home AV set ups, I had to use a non powered 🤷♂️🤝