Fix flaky stats-batch tests and extend Crucible E2E LOTL coverage.

Stop the stats batch timer in unit tests before reading pending coalesced state, teach the Playwright stub agent to emit lotl_tier stats, and prefer server/webroot so phase-8 E2E serves the current frontend build.

server/web/e2e/stub-agent.ts

@@ -6,6 +6,11 @@
 export const E2E_STUB_AGENT_ID = 'e2e-crucible-agent';
 export const E2E_STUB_AGENT_HOSTNAME = 'E2E-Crucible-Host';
 export const E2E_WHOAMI_RESPONSE = 'e2e-whoami-ok';
+/** Active LOTL tier sent in stub stats — maps to "LOTL In-Process" in Crucible. */
+export const E2E_STUB_LOTL_TIER = 'inprocess';
+export const E2E_STUB_LOTL_BADGE = 'LOTL In-Process';
+
+const E2E_STUB_STATS_INTERVAL_MS = 1_000;
 
 type HubMessage = {
   type: string;
@@ -28,6 +33,26 @@ function send(ws: WebSocket, type: string, payload: Record<string, unknown>): vo
   ws.send(JSON.stringify({ type, payload }));
 }
 
+function sendStubStats(ws: WebSocket): void {
+  send(ws, 'stats', {
+    hashrate_15s: 42,
+    hashrate_1m: 42,
+    hashrate_15m: 42,
+    shares_submitted: 0,
+    shares_accepted: 0,
+    cpu_usage_pct: 5,
+    memory_usage_pct: 40,
+    uptime_seconds: 120,
+    active_method: 'inprocess',
+    mining_hashrate: 42,
+    lotl_tier: E2E_STUB_LOTL_TIER,
+    lotl_attempts: [
+      { tier: 'container', ok: false, error: 'e2e-no-docker', duration_ms: 100 },
+      { tier: 'inprocess', ok: true, duration_ms: 200 },
+    ],
+  });
+}
+
 function replyCommand(ws: WebSocket, action: string, command: string): void {
   let message = 'e2e-stub-ok';
   if (action === 'resume') {
@@ -88,6 +113,9 @@ export async function connectStubAgent(
     }, { once: true });
   });
 
+  sendStubStats(ws);
+  const statsTimer = setInterval(() => sendStubStats(ws), E2E_STUB_STATS_INTERVAL_MS);
+
   ws.addEventListener('message', (ev) => {
     let msg: HubMessage;
     try {
@@ -103,6 +131,7 @@ export async function connectStubAgent(
   });
 
   return () => {
+    clearInterval(statsTimer);
     ws.close();
   };
 }