Yes, it sounds like this is the case.
As Jay mentioned above, we do not allow custom plugins to be installed on any plan other our Enterprise plans.
Yes, on our Standard and Business plans, customers can use the API as well as install themes, and theme components (which in many ways can be thought of as “front end plugins”, but I don’t think that’s what you’re looking for here).
API documentation is here: https://docs.discourse.org/, and more general developer docs start here: Introduction to Discourse Development
The outline of your plan for doing this via an API integration sounds reasonable to me – that said…
…this may be worth exploring.
The Discourse Automation plugin is available on our Business plan and is worth taking a look at: Discourse Automation
There are built-in “triggers” and “scripts” – it may have exactly what you need, or if you find it’s missing something, it may be relatively straightforward to contribute that missing piece to the plugin.
I think that’s where I’d start looking…
That said, another thing worth looking at if you’re exploring this territory is Discourse AI, which Automation can also integrate with. An example of that is AI triage.
AI features are backed by Personas, which can implement custom tools. So you could implement a tool that calls your API, for example. The persona could then be called by automation. Or you could associate a user with the persona and allow community members within a certain group to call it directly.