It's possible to get transparency output by modifying the URP UberPost.shader by replacing the line:
return half4(color, 1.0);
with:
half alpha = SAMPLE_TEXTURE2D_X(_BlitTexture, sampler_LinearClamp, uvDistorted).w;
return half4(color, alpha);
Then as long as you have a duplicate camera outputting to a render texture using background color rgba 0,0,0,0 (make sure you turn off the audio listener or you will leak memory), you can use that texture in the spout sender with alpha and OBS will pick it up under premultiplied alpha mode.