feat(gateway): inject timestamps into agent handler messages

Messages arriving through the gateway agent method (TUI, web, spawned
subagents, sessions_send, heartbeats) now get a timestamp prefix
automatically. This gives all agent contexts date/time awareness
without modifying the system prompt (which is cached for stability).

Channel messages (Discord, Telegram, etc.) already have timestamps
via envelope formatting in a separate code path and never reach
the agent handler, so there is no double-stamping risk.

Cron jobs also inject their own 'Current time:' prefix and are
detected and skipped.

Extracted as a pure function (injectTimestamp) with 12 unit tests
covering: timezone handling, 12/24h format, midnight boundaries,
envelope detection, cron detection, and empty messages.

Integration test verifies the agent handler wires it in correctly.

Closes #3658
Refs: #1897, #1928, #2108

src/gateway/server-methods/agent-timestamp.ts

@@ -0,0 +1,69 @@
+import {
+  formatUserTime,
+  resolveUserTimeFormat,
+  resolveUserTimezone,
+} from "../../agents/date-time.js";
+import type { MoltbotConfig } from "../../config/types.js";
+
+/**
+ * Envelope pattern used by channel plugins (Discord, Telegram, etc.):
+ *   [Channel sender 2026-01-28 20:31 EST] message text
+ *
+ * Messages arriving through channels already have timestamps.
+ * We skip injection for those to avoid double-stamping.
+ */
+const ENVELOPE_PATTERN = /^\[[\w]+ .+ \d{4}-\d{2}-\d{2}/;
+
+/**
+ * Cron jobs inject "Current time: ..." into their messages.
+ * Skip injection for those too.
+ */
+const CRON_TIME_PATTERN = /Current time: /;
+
+export interface TimestampInjectionOptions {
+  timezone?: string;
+  timeFormat?: "12" | "24";
+  now?: Date;
+}
+
+/**
+ * Injects a timestamp prefix into a message if one isn't already present.
+ *
+ * Used by the gateway agent handler to give all agent contexts (TUI, web,
+ * spawned subagents, sessions_send, heartbeats) date/time awareness without
+ * modifying the system prompt (which is cached for stability).
+ *
+ * Channel messages (Discord, Telegram, etc.) already have timestamps via
+ * envelope formatting and take a separate code path — they never reach
+ * the agent handler, so there's no double-stamping risk.
+ *
+ * @see https://github.com/moltbot/moltbot/issues/3658
+ */
+export function injectTimestamp(message: string, opts?: TimestampInjectionOptions): string {
+  if (!message.trim()) return message;
+
+  // Already has a channel envelope timestamp
+  if (ENVELOPE_PATTERN.test(message)) return message;
+
+  // Already has a cron-injected timestamp
+  if (CRON_TIME_PATTERN.test(message)) return message;
+
+  const now = opts?.now ?? new Date();
+  const timezone = opts?.timezone ?? "UTC";
+  const timeFormat = opts?.timeFormat ?? "12";
+
+  const formatted = formatUserTime(now, timezone, resolveUserTimeFormat(timeFormat));
+  if (!formatted) return message;
+
+  return `[${formatted}] ${message}`;
+}
+
+/**
+ * Build TimestampInjectionOptions from a MoltbotConfig.
+ */
+export function timestampOptsFromConfig(cfg: MoltbotConfig): TimestampInjectionOptions {
+  return {
+    timezone: resolveUserTimezone(cfg.agents?.defaults?.userTimezone),
+    timeFormat: cfg.agents?.defaults?.timeFormat as "12" | "24" | undefined,
+  };
+}