As I mentioned in another comment — I used jQuery, and chose not to share anything because I don't need everyone's feedback on how old and dumb that makes me. :)

But basically, anything you can render in a browser can happen on the screen. Get JavaScript to show your current time in a browser, then pull in that URL into your OBS scene. The background will be transparent.

I think it's using Blink to render things underneath, that's what it seems like at least.