The notification service I use is Pushover. Pushover notifications can be triggered by post requests (in effect a type of webhook). But, you have to open the notification to then show the actionable URL to be able to run it and have a shortcut launched.
I would say Pushover has broad multi-platform broadcast utility while Pushcut is tailored for an improved Shortcuts and i*OS experience around this particular remote trigger of a shortcut feature. Pushcut obviously also has local scheduling, etc. which is out of scope for Pushover.
Also, a bit of a sneak peak of the planned future features:
Trigger HomeKit scenes from notification actions
Run webhook URL as background operations from notifications (eg: trigger IFTTT webhook without opening a browser)
Apple Watch support for notifications
The problem with the Watch:
you can’t run shortcuts on the watch, and you can’t open app urls on the watch (afaik).
but for webhooks, online actions, and HomeKit it should work just fine.
any thoughts - do you think an watch app will be to confusing if only “half” the actions work on it?