feat: add diagnostic web app shell

.planning/phases/007-web-app-shell-diagnostic-start/007-RESEARCH.md

@@ -0,0 +1,27 @@
+# Phase 7 Research: Web App Shell and Diagnostic Start
+
+## Findings
+
+The existing Go backend can serve static assets without adding frontend build
+tooling. For the first MVP UI, plain HTML/CSS/JavaScript is enough and keeps
+the repo dependency-light.
+
+The diagnostic APIs already provide all Phase 7 data:
+
+- `POST /api/v1/diagnostic-sessions`
+- `POST /api/v1/diagnostic-sessions/{id}/answers`
+- `GET /api/v1/diagnostic-sessions/{id}`
+
+## Recommended Shape
+
+- Add `internal/webapp` with embedded static assets.
+- Register web app routes from `httpapi.Handler`.
+- Keep frontend files small and focused.
+- Use fetch calls directly against existing API routes.
+
+## Risks
+
+- A mock UI would not prove the backend loop. The UI must call real APIs.
+- A marketing-style landing page would distract from the core product surface.
+- Overbuilding a frontend stack before interaction validation would violate
+  YAGNI.