But now I want to add a JSON API to the program: I could reuse the same routes (/create, etc), but require an application+json header; or add a full /api/ component essentially duplicating the logic from the main app.
Neither option is great.
That's what we did and it works pretty well in practice.
As a result for POST requests you have to have htmx routes that accept urlencode and API routes that accept JSON, and JSON is far superior. But for outputs I actually think separating your UI and API is helpful. The code reuse is not worth the entanglement of concerns.