You might use the Advanced Scene Switcher plugin for that.
This plugin will allow you to automate various tasks using "Macros". Macros consist of a list of conditions under which a list of actions will be performed. Examples and guides can be found in the wiki. Feel free to contribute! If you run...
obsproject.com
It'll also do Websockets, and there's a Run action too, that can call any external program with arguments that you supply.
The "only on change" checkbox prevents it from running repeatedly while the condition remains true. The default is unchecked, but I always have mine checked.
There's also a "Stream stopping" condition. Not sure what the difference is.
Or you could do this:
That creates a named hotkey that you can then bind in OBS's normal settings for hotkeys. Hit that *instead of* the Stop Streaming button, and it'll do both. You might even reverse the order of actions and add a Wait in between, so that the HTTP happens some time before the stream stops, but all you need to think about as an operator is the correct way *for your rig* to stop the stream.
And of course, you can automate a ton of other stuff too. One of my rigs has maybe 30 different macros that collectively take care of everything, except the art itself of covering a live event. (you can't automate art)