feat: add model picker to Analysis and Batch pages with full backend wiring

Thread the optional model parameter through the entire analysis pipeline:
- analyzer.py: analyze_company, _analyze_company_safe, analyze_companies,
  and analyze_single_patent now accept and forward model override
- api.py: single company endpoint accepts model query param; batch and
  async batch endpoints pass request.model through to the analyzer
- client.ts: analyzeCompany, analyzeBatch, analyzeBatchAsync accept model;
  add listModels() to fetch available models from GET /models
- Analysis.tsx: add model selector dropdown that loads from /models API
- Batch.tsx: add model selector alongside the workers slider

Users can now pick a specific LLM (GPT-4o, Claude 3.5, Gemini, etc.)
per analysis request, or leave it on the server default.

Closes leeworks-agents/SPARC#351

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

frontend/src/pages/Batch.tsx

@@ -1,5 +1,5 @@
 import { useState } from 'react';
-import { useMutation } from '@tanstack/react-query';
+import { useMutation, useQuery } from '@tanstack/react-query';
 import { analysisApi } from '../api/client';
 import { Rocket, CheckCircle, AlertCircle, ChevronDown, ChevronUp } from 'lucide-react';
 import { BarChart, Bar, XAxis, YAxis, Tooltip, ResponsiveContainer, Cell } from 'recharts';
@@ -8,12 +8,18 @@ import type { BatchAnalysisResult } from '../types';
 export function Batch() {
   const [companiesInput, setCompaniesInput] = useState('');
   const [maxWorkers, setMaxWorkers] = useState(3);
+  const [selectedModel, setSelectedModel] = useState('');
   const [result, setResult] = useState<BatchAnalysisResult | null>(null);
   const [expandedItems, setExpandedItems] = useState<Set<string>>(new Set());
 
+  const modelsQuery = useQuery({
+    queryKey: ['models'],
+    queryFn: () => analysisApi.listModels(),
+  });
+
   const mutation = useMutation({
     mutationFn: ({ companies, workers }: { companies: string[]; workers: number }) =>
-      analysisApi.analyzeBatch(companies, workers),
+      analysisApi.analyzeBatch(companies, workers, selectedModel || undefined),
     onSuccess: (data) => setResult(data),
   });
 
@@ -85,6 +91,29 @@ export function Batch() {
             <div className="text-center text-text-primary font-semibold">{maxWorkers}</div>
           </div>
 
+          <div>
+            <label className="block text-sm font-medium text-text-secondary mb-2">
+              LLM Model
+            </label>
+            <div className="relative">
+              <select
+                value={selectedModel}
+                onChange={(e) => setSelectedModel(e.target.value)}
+                className="w-full appearance-none bg-bg-card/80 border border-primary/30 rounded-lg pl-3 pr-8 py-2 text-sm text-text-primary focus:outline-none focus:border-primary focus:ring-2 focus:ring-primary/20 transition-all cursor-pointer"
+              >
+                <option value="">
+                  {modelsQuery.data ? `Default (${modelsQuery.data.default})` : 'Default'}
+                </option>
+                {modelsQuery.data?.models.map((m) => (
+                  <option key={m.id} value={m.id}>
+                    {m.name} ({m.provider})
+                  </option>
+                ))}
+              </select>
+              <ChevronDown className="absolute right-2 top-1/2 -translate-y-1/2 text-text-secondary pointer-events-none" size={16} />
+            </div>
+          </div>
+
           <button
             type="submit"
             disabled={mutation.isPending || !companiesInput.trim()}