I wasn't aware that any phone had an HDMI out. Though I guess it's possible, since the vast majority of their single USB ports support USB OTG, to put a USB -> HDMI adapter there and have it drive a display or capture card or whatever. Then it becomes a question of how the phone works, not OBS, to put the right signal on that wire for OBS to pick up, and that would be a question for the phone support, not here.
Or, if you're okay with the general unreliability of WiFi (can't use it in a crowd, etc.), or you have a WiFi network that *you* control access to, without many neighbors to interfere with the radio signal, then you might use the IP Webcam app for Android:
Turn your phone into a wireless camera!
play.google.com
It's free with ads, but the ads are only on the phone screen, not the video feed. It has an overlay on the bottom of the phone screen to tell you where to point a web browser. Once you have that working - full-screen in a standalone web browser - then you can copy the completed URL that it came up with, and paste it into a browser source in OBS.
If you start the app first and then OBS, then it comes right up.
If you start OBS first and then the app, then you'll need to refresh the browser source before it works.
