fix(router): make the real embedder + TurboVec L3 actually work end-to-end

- LlamaCppEmbedder: parse llama.cpp --pooling mean nested response [[...]] (was
  silently failing every embed with 'unexpected response shape')
- qa-stack: embedder -b/-ub 8192 so docs >512 tokens don't 500; fix default path
- TurboVecL3MemoryStore: send init handshake on startup (was 'Index not initialized'
  on every add/query)
- turbovec_sidecar.py: rewrite add/search/save/load against the real turbovec API
  (batched ndarray, L2-normalize so IP=cosine, prepare() before search, classmethod
  load). The sidecar was scaffolding never run against the real lib.

infrastructure/inference/llama_cpp/src/main/kotlin/com/correx/infrastructure/inference/llama/cpp/LlamaCppEmbedder.kt

@@ -116,6 +116,15 @@ class LlamaCppEmbedder(
             return arrayResult
         }
 
+        // llama.cpp --pooling mean: [{"embedding": [[...]]}] (nested list-of-one-vector).
+        val nestedResult = runCatching {
+            json.decodeFromString<List<EmbeddingNestedArrayResponse>>(responseBody)
+                .firstOrNull()?.embedding?.firstOrNull().orEmpty()
+        }.getOrNull()
+        if (nestedResult != null && nestedResult.isNotEmpty()) {
+            return nestedResult
+        }
+
         throw IllegalStateException(
             "Unexpected embedding response shape from $url. " +
                 "Response body (first 200 chars): ${responseBody.take(200)}"

infrastructure/inference/llama_cpp/src/main/kotlin/com/correx/infrastructure/inference/llama/cpp/LlamaCppEmbeddingApiModels.kt

@@ -19,6 +19,13 @@ data class EmbeddingArrayResponse(
     val embedding: List<Float>,
 )
 
+// llama.cpp /embedding with --pooling mean returns a list-of-one-vector per item:
+// [{"index":0,"embedding":[[floats...]]}]. embedding is nested, not flat.
+@Serializable
+data class EmbeddingNestedArrayResponse(
+    val embedding: List<List<Float>>,
+)
+
 @Serializable
 data class OpenAiEmbeddingData(
     val embedding: List<Float>,

infrastructure/inference/llama_cpp/src/test/kotlin/com/correx/infrastructure/inference/llama/cpp/LlamaCppEmbedderTest.kt

@@ -79,6 +79,28 @@ class LlamaCppEmbedderTest {
         assert(kotlin.math.abs(result[2] - 0.7f) < 0.0001f)
     }
 
+    @Test
+    fun `embed parses llama-cpp nested pooling-mean array format`(): Unit = runBlocking {
+        // llama.cpp /embedding with --pooling mean: [{"index":0,"embedding":[[...]]}]
+        val mockEngine = MockEngine {
+            respond(
+                content = """[{"index":0,"embedding":[[0.5,0.6,0.7]]}]""",
+                headers = headersOf(HttpHeaders.ContentType, ContentType.Application.Json.toString())
+            )
+        }
+        val embedder = LlamaCppEmbedder(
+            url = "http://localhost:11000",
+            dimension = 3,
+            httpClient = HttpClient(mockEngine),
+        )
+
+        val result = embedder.embed("test text")
+
+        assert(result.size == 3)
+        assert(kotlin.math.abs(result[0] - 0.5f) < 0.0001f)
+        assert(kotlin.math.abs(result[2] - 0.7f) < 0.0001f)
+    }
+
     @Test
     fun `embed throws on dimension mismatch`(): Unit = runBlocking {
         val mockEngine = MockEngine { request ->