When setting up a custom Alexa skill, we direct our AWS fulfillment script to /api/alexa
I use the Nabu Casa cloud integration for communication with Alexa. It would be great if I could have the option to use the Nabu Casa cloud to trigger intent scripts so that I wouldn’t also need the Alexa component.
This might also work for Google/dialogflow.
You can’t do this already? Color me surprised. I thought everything with alexa smart home skill was a part of cloud.
The possibility that I’m ignorant is not out of the question 
Well… I’m in the same boat. I haven’t set it up in 5 years, I don’t even know if my intents work anymore. I found it too cumbersome to say “Alexa, ask home assistant to xyz”. They are still set up I believe but I don’t know if they work as I haven’t used them in 5 years. I find it much easier to create routines with nice phrases over intents.
Either way, I assumed there was a method to set this up through cloud, but I don’t use cloud. I use the alexa smart home skill.
I still use the skill for a couple of things that routines can’t handle. For example (I call my HA instance “Dexter”):
Alexa, ask Dexter to add beer to the shopping list. (adds item to the Shopping List integration using shopping_list.add_item service)
Alexa, ask Dexter to play Discover Weekly
Alexa, ask Dexter to play Snoozy
(etc - names of Spotify playlists from a curated list)
Those don’t work so well with routines since routines can’t handle a “variable” (unless I’m also ignorant there!)