feat: add diagnostic web app shell

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

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+# Phase 7 Plan: Web App Shell and Diagnostic Start
+
+**Status:** Ready for execution
+**Phase Goal:** Create a working diagnostic web app shell.
+
+## Tasks
+
+### 1. Serve embedded web app
+
+- Add `internal/webapp`.
+- Embed static app assets.
+- Register root and asset routes through the existing Go server.
+
+### 2. Build diagnostic UI
+
+- Add setup form for user id, target role, stack, and interview timeline.
+- Create diagnostic session through the real API.
+- Show returned questions.
+
+### 3. Build answer and grading UI
+
+- Let user select a question.
+- Submit answer through the real API.
+- Show overall grade, scores, follow-up, and evidence.
+
+### 4. Verify
+
+- Add HTTP tests for root web app and asset serving.
+- Run Go tests, OpenSpec validation, line-count check.
+- Smoke the rendered app endpoint and diagnostic API flow.
+
+## Out of Scope
+
+- Frontend build tooling.
+- Authentication.
+- Phase 8 progress panels.