feat(backend): wire Ollama LLM for context messages (TODO-005)

Dual-path LLM enrichment for AI context prep messages:
1. extraction-service (if EXTRACTION_SERVICE_URL set)
2. Ollama direct (if OLLAMA_URL set) — non-streaming /api/generate
3. Keyword rules fallback
4. Generic fallback

New env vars: OLLAMA_URL, OLLAMA_MODEL (default: gemma3:4b)
Both LLM paths use 5s timeout and null-return-on-error pattern.
Feature-gated behind ai_context_messages.enabled flag.

backend/src/lib/ai-context.ts

@@ -56,25 +56,13 @@ export interface ContextMessageResult {
   source: 'llm' | 'keyword' | 'generic';
 }
 
-// ── LLM enrichment (extraction-service or ollama-client) ──
+// ── LLM enrichment (dual path: extraction-service or Ollama) ──
 
-// TODO-005: Wire real LLM enrichment for context messages
-// Priority: high | Phase: A.4
-// Replace the stub below with a real LLM call. Two options:
-//   Option A: @bytelyst/extraction client — POST to extraction-service /api/extract
-//     with task='timer-context'. Requires creating a new extraction task type in
-//     learning_ai_common_plat/services/extraction-service/src/modules/extract/.
-//   Option B: @bytelyst/ollama-client — call Ollama directly with buildPrompt().
-//     Simpler, no extraction-service dependency, but no task abstraction.
-// The prompt is already built by buildPrompt() below. Just replace the fetch stub
-// with a real client call. Keep the 5s timeout and null-return-on-error pattern.
-async function llmEnrich(input: ContextMessageInput): Promise<string | null> {
-  // Only attempt if extraction service URL is configured
+async function llmViaExtraction(prompt: string): Promise<string | null> {
   const extractionUrl = config.EXTRACTION_SERVICE_URL;
   if (!extractionUrl) return null;
 
   try {
-    const prompt = buildPrompt(input);
     const res = await fetch(`${extractionUrl}/api/extract`, {
       method: 'POST',
       headers: { 'Content-Type': 'application/json' },
@@ -85,9 +73,7 @@ async function llmEnrich(input: ContextMessageInput): Promise<string | null> {
       }),
       signal: AbortSignal.timeout(5_000),
     });
-
     if (!res.ok) return null;
-
     const data = await res.json() as { result?: string };
     return data.result ?? null;
   } catch {
@@ -95,6 +81,37 @@ async function llmEnrich(input: ContextMessageInput): Promise<string | null> {
   }
 }
 
+async function llmViaOllama(prompt: string): Promise<string | null> {
+  const ollamaUrl = config.OLLAMA_URL;
+  if (!ollamaUrl) return null;
+
+  try {
+    const res = await fetch(`${ollamaUrl}/api/generate`, {
+      method: 'POST',
+      headers: { 'Content-Type': 'application/json' },
+      body: JSON.stringify({
+        model: config.OLLAMA_MODEL,
+        prompt,
+        stream: false,
+        options: { num_predict: 80, temperature: 0.7 },
+      }),
+      signal: AbortSignal.timeout(5_000),
+    });
+    if (!res.ok) return null;
+    const data = await res.json() as { response?: string };
+    const text = data.response?.trim();
+    return text && text.length > 5 ? text : null;
+  } catch {
+    return null;
+  }
+}
+
+async function llmEnrich(input: ContextMessageInput): Promise<string | null> {
+  const prompt = buildPrompt(input);
+  // Try extraction-service first, then Ollama
+  return await llmViaExtraction(prompt) ?? await llmViaOllama(prompt);
+}
+
 function buildPrompt(input: ContextMessageInput): string {
   const parts = [
     `Timer: "${input.timerLabel}" fires in ${input.minutesBefore} minutes.`,

backend/src/lib/config.ts

@@ -15,6 +15,8 @@ const envSchema = baseBackendConfigSchema.extend({
   FIELD_ENCRYPT_MEK_NAME: z.string().default('chronomind-mek'),
   AZURE_KEYVAULT_URL: z.string().optional(),
   EXTRACTION_SERVICE_URL: z.string().optional(),
+  OLLAMA_URL: z.string().optional(),
+  OLLAMA_MODEL: z.string().default('gemma3:4b'),
 });
 
 export const config = envSchema.parse(process.env);