feat(backend): resume + venv PATH + end-to-end F1 smoke (fake-pi-rpc)

- Add PiProcessManager.resume(sessionId, tht): reads provider/model/thinking
  from tht.sessionShow() and calls spawnFor with those values
- Add POST /sessions/:id/resume route: calls mgr.resume then re-wires
  bridge.onClientEvent → hub.publish
- Confirm venv PATH already present in real spawn (no change needed)
- Add e2e test: POST /sessions → SSE receives ui_request via pendingWidget
  re-emit → POST /sessions/s1/response → 204 (all over real HTTP against
  fake-pi-rpc)

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

backend/test/e2e-f1.test.ts

@@ -0,0 +1,49 @@
+import { test, expect } from "vitest";
+import { spawn } from "node:child_process";
+import path from "node:path";
+import { buildApp } from "../src/app.js";
+import { loadConfig } from "../src/config.js";
+
+const FAKE = path.resolve("../harness/tests/fake_pi/fake_pi_rpc.mjs");
+const SCRIPT = path.resolve("../harness/tests/fake_pi/scripts/f1_disambiguation.json");
+
+test("loop F1: crea sessione → SSE riceve il widget → risponde → 204", async () => {
+  const app = buildApp(loadConfig({ THT_HARNESS_DIR: "../harness" }), {
+    thtRunner: {
+      sessionNew: async () => ({ id: "s1" }),
+      sessionShow: async (_id: string) => ({ id: "s1", provider: undefined, model: undefined, thinking: undefined }),
+      sessionList: async () => [],
+    } as any,
+    spawnFn: () => spawn("node", [FAKE, SCRIPT]) as any,
+  });
+  await app.listen({ port: 0, host: "127.0.0.1" });
+  const base = `http://127.0.0.1:${(app.server.address() as any).port}`;
+
+  // 1. Create session — spawns fake-pi, sends prompt, fake-pi emits widget
+  await fetch(`${base}/sessions`, {
+    method: "POST",
+    headers: { "content-type": "application/json" },
+    body: JSON.stringify({ workspace: "w", question: "q" }),
+  });
+
+  // 2. Small delay to let fake-pi process the prompt and fill pendingWidget
+  await new Promise((r) => setTimeout(r, 50));
+
+  // 3. SSE: read the first event (pendingWidget re-emit via subscribe)
+  const es = await fetch(`${base}/sessions/s1/events`);
+  const reader = es.body!.getReader();
+  const chunk = await reader.read();
+  const text = new TextDecoder().decode(chunk.value);
+  expect(text).toContain("ui_request");
+  await reader.cancel();
+
+  // 4. POST response — widget id is "u1" from f1_disambiguation.json
+  const resp = await fetch(`${base}/sessions/s1/response`, {
+    method: "POST",
+    headers: { "content-type": "application/json" },
+    body: JSON.stringify({ ui_response: { id: "u1", choices: ["a"] } }),
+  });
+  expect(resp.status).toBe(204);
+
+  await app.close();
+}, 10000);