feat: rolling conversation summary + session continuity

- Backend emits session id in SSE; frontend sets activeChat so follow-ups
  reuse the same session (fixes fragmented history).
- sessions.summary column; messages past RECENT_LIMIT (10) are folded into
  a persisted summary via a non-streaming model call.
- buildMessages sends system(+summary) + last 10 messages, bounding context
  while preserving long-range memory.
- Tests: aiMessages (capping + summary injection).

backend/test/aiMessages.test.js

@@ -0,0 +1,33 @@
+import test from "node:test";
+import assert from "node:assert/strict";
+import { buildMessages, RECENT_LIMIT } from "../src/services/ai.js";
+
+function msg(role, i) {
+  return { id: String(i), session_id: "s", role, text: `${role}-${i}`, created_at: new Date(i).toISOString() };
+}
+
+test("caps message history to the recent window", () => {
+  const history = Array.from({ length: RECENT_LIMIT + 5 }, (_, i) => msg(i % 2 ? "assistant" : "user", i));
+  const built = buildMessages(history, "Grade 10", "math", "c", "");
+  // system + RECENT_LIMIT messages
+  assert.equal(built.length, 1 + RECENT_LIMIT);
+  assert.equal(built[0].role, "system");
+  // the newest message is included
+  assert.equal(built[built.length - 1].content, "user-" + (RECENT_LIMIT + 4));
+  // the oldest message is dropped
+  assert.ok(!built.some((m) => m.content === "user-0"));
+});
+
+test("injects the summary into the system prompt when present", () => {
+  const history = [msg("user", 0), msg("assistant", 1)];
+  const built = buildMessages(history, "Grade 6", "english", "c5", "Student is in Grade 6 English.");
+  assert.equal(built[0].role, "system");
+  assert.ok(built[0].content.includes("Student is in Grade 6 English."));
+  // still includes the messages
+  assert.equal(built.length, 3);
+});
+
+test("does not inject an empty summary", () => {
+  const built = buildMessages([msg("user", 0)], "g", "s", "c", "");
+  assert.ok(!built[0].content.includes("Earlier in this conversation:"));
+});