@Tanner write API could help with that, but until then, here's the high-level implementation/workaround:
FTPP (form-to-post plugin) establishes new POST route at /feedback
When that route is called, take req.body.text (where text is the id in the corresponding form) and call Topic.post as a pre-registered user.
That's pretty much it. There's more to expand on (such as spam prevention/throttling/auth/security), but yeah.
Please provide reproduction steps. For example on this forum the Testing Ground category is not visible to guests. https://community.nodebb.org/category/4/testing-ground. So if you browse this forum as a guest it doesn't show up on /recent and it won't be visible in the category dropdown on that page either.
Your quick reply (and example) made it easier for us to identify it as a layer 8 problem. Our subcategories did not have the expected rights. Sorry for raising this as a bug!