feat(cli): add --json output flag to doctor, models, route, run, and analytics (#13)

- Adds optional `--json` / `-j` flag to CLI commands for scriptable output
- Redirects non-JSON logging messages to stderr under JSON mode
- Adds test suite for CLI JSON serialization in backend/tests/test_cli.py
- Updates documentation in README.md

backend/tests/test_cli.py

@@ -0,0 +1,46 @@
+import json
+import pytest
+from typer.testing import CliRunner
+from app.cli.main import app
+
+runner = CliRunner()
+
+def test_cli_doctor_json():
+    result = runner.invoke(app, ["doctor", "--json"])
+    assert result.exit_code == 0
+    data = json.loads(result.stdout)
+    assert "python" in data
+    assert "database" in data
+    assert "mock_engine" in data
+
+def test_cli_models_json():
+    result = runner.invoke(app, ["models", "--json"])
+    assert result.exit_code == 0
+    data = json.loads(result.stdout)
+    assert isinstance(data, list)
+    if len(data) > 0:
+        assert "id" in data[0]
+        assert "provider" in data[0]
+
+def test_cli_route_json():
+    result = runner.invoke(app, ["route", "test prompt", "--json"])
+    assert result.exit_code == 0
+    data = json.loads(result.stdout)
+    assert "selected_model" in data
+    assert "estimated_latency_ms" in data
+
+def test_cli_run_json():
+    result = runner.invoke(app, ["run", "test prompt", "--json"])
+    assert result.exit_code == 0
+    data = json.loads(result.stdout)
+    assert "decision" in data
+    assert "response" in data
+    assert "fallback" in data
+
+def test_cli_analytics_json():
+    result = runner.invoke(app, ["analytics", "--json"])
+    assert result.exit_code == 0
+    data = json.loads(result.stdout)
+    assert "total_requests" in data
+    assert "avg_latency_ms" in data
+    assert "savings" in data