You’re not using the REST API correctly for calling a service. You need to specify both domain and service in the URL, as well as service data (if needed.) And it needs to use the POST methond. See REST API Call Service.
What are you trying to “toggle”? Or are you trying to do something else?
Domain is the part before the “dot”. E.g., to turn on a light you call light.turn_on - light is the domain, and turn_on is the service. If you’re trying to run a script, then script is the domain, and the name of the script is the service - e.g., script.my_script. When using the REST API, you do it like this: .../api/services/script/my_script....
I can’t tell if the POST method is selected because you didn’t show all the details of your webhook.
EDIT: Oh, didn’t realize it was a bigger picture I needed to click on.
Ok, this one looks correct. For a script there are two ways to run it. The first is using script as the domain and the name of the script as the service: .../api/services/script/gaming.... The other is to use .../api/services/script/turn_on... and then include the entity_id of the script as you did here.
So, there must be a typo somewhere. Try doing it with curl, and then once you get that working transfer the details to the webhook.