feat: add fee workspace and polish AI presentation

.trellis/tasks/07-09-ai-fee-frontend/implement.md

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+# AI Presentation And Fee Workspace Implementation Plan
+
+## 1. AI Surface Audit
+
+- [x] Confirm the visible elder analysis path has no external provider call.
+- [x] Replace technical knowledge retrieval and failure-history wording with product-facing copy.
+- [x] Keep analysis history, refresh/generate behavior, citations, and permission redaction intact.
+- [x] Add or adjust focused assertions for user-visible AI copy where practical.
+
+## 2. Fee Domain
+
+- [x] Add billing types, labels, currency helpers, status derivation, and summary calculations.
+- [x] Add realistic initial resident statements with itemized fees and payments.
+- [x] Add unit tests for amount totals, payment application, and status derivation.
+
+## 3. Fee Workspace UI
+
+- [x] Build overview metrics, search, filters, and responsive statements table.
+- [x] Build statement detail with charge items and payment history.
+- [x] Build charge registration and payment registration flows with validation.
+- [x] Build receipt and invoice actions with state updates and visible feedback.
+
+## 4. Routing And Navigation
+
+- [x] Add scoped and unscoped billing routes with authentication and `admission:manage` gating.
+- [x] Add `费用管理` and a Lucide icon to the operations navigation.
+- [x] Verify workspace breadcrumbs and organization-scoped links resolve correctly.
+
+## 5. Validation
+
+- [x] Run focused billing and AI tests.
+- [x] Run `pnpm lint`.
+- [x] Run `pnpm type-check`.
+- [x] Run `pnpm test`.
+- [x] Run `pnpm build`.
+- [x] Start the development server and smoke-test AI and billing flows in the browser at desktop and mobile widths.
+- [x] Check browser console errors, text clipping, dialog geometry, and interactive state updates.
+
+## Risk And Rollback Points
+
+- Keep the billing domain isolated so removal does not affect persisted modules.
+- Do not change `Permission`, role seed, schema, or migrations for the frontend-only workspace.
+- Reuse `admission:manage`; changing authorization is out of scope.
+- Do not alter AI API response shapes or stored analysis records.