Automated YouTube chat Browser source

I'm looking for some sort of way to automatically update a Browser source URL whenever I start a new stream on YouTube. I can see that the built in YouTube chat dock in OBS automatically gets updated to the correct current chat url when a new stream is started.

Today I have to manually copy the current chat URL ("Copy current address" from the chat dock) and paste it into my Browser source, whenever I want to display my Browser source, that shows chat on my scenes.

Is there any way via a script to automatically update the Browser source URL from the chat dock, whenever the URL in the dock is changed?

Hey, not sure if you still need this, but for posterity, there is a LUA script plugin that does this.

You just need to download the LUA script, add it from the script menu option, and then specify 1) Your youtube URL and 2) The names of the Browser Sources to update. The Git page explains it fairly well.