I''ve been trying to connect my PS4 Pro to my Acer X1230PS projector (https://www.cnet.com/products/acer-x1230ps-dlp-pro
I've been using the projector and converter with my Xbox One for years, with no problems, even at maximum resolution (the projector converts 1080p to fit its 1024x768 screen). With the PS4 Pro, I've tried all graphics settings (Automatic,1080p, 1080i and 720p, as well as Limited RGB), but I haven't been able to get an image. I've also tried disabling HDCP, though I've got no idea whether that could be expected to do anything. Weirdly, the projector does keep bringing up its 'Processing signal - please wait' message every couple of minutes, but then it goes back to 'No signal' before any image appears.
PS4 Settings, System, Enable HDCP, turn this off.
HDMI to analog conversion like VGA don't support HDCP.
What kind of HDMI to VGA converter you using? Powered by wall outlet?
If converter is not powered by wall outlet, PS4 might not provide enough HDMI power for converter to work without external power, and might require putting in HDMI device powered by wall outlet in between converter and PS4. It can be HDMI switch, splitter, matrix, audio extractor, or audio receiver.