Had same laptop issue (graphics card not powerful enough) so I run the app on my iPhone and connect with a 3-way adapter - adapter plugs to the phone, 2 "outlets" on other side of adapter take an HDMI cable that goes to the TV and other socker takes a regular iPhone charger cable.
I have a Wahoo Kickr but if your goal is to bypass the laptop then that might work - then I guess your phone/Zwift needs to pick up either HR or watts some how.
Here’s the two things I have:
-yellow cable HDMI / HDMI both male
-white adapter iPhone male/HDMI female + iPhone female