fix(system-prompt): hint session_status for date/time instead of embedding it

The system prompt intentionally excludes the current date/time for cache
stability (see 66eec295b). This leaves agents without date awareness,
causing wrong day-of-week claims (#1897, #1928, #2108).

Instead of reverting the cache optimization, add a one-line hint directing
agents to use session_status when they need the current date/time. This
keeps the prompt stable while teaching frontier models where to look.

Also adds a negative test ensuring the date/time is NOT re-added to the
system prompt, with comments explaining why and pointing to #3658 for the
complementary gateway-level timestamp injection approach.

Refs: #1897, #1928, #3658

src/agents/system-prompt.test.ts

@@ -171,6 +171,41 @@ describe("buildAgentSystemPrompt", () => {
     expect(prompt).toContain("Time zone: America/Chicago");
   });
 
+  it("hints to use session_status for current date/time", () => {
+    const prompt = buildAgentSystemPrompt({
+      workspaceDir: "/tmp/clawd",
+      userTimezone: "America/Chicago",
+    });
+
+    expect(prompt).toContain("session_status");
+    expect(prompt).toContain("current date");
+  });
+
+  // The system prompt intentionally does NOT include the current date/time.
+  // Only the timezone is included, to keep the prompt stable for caching.
+  // See: https://github.com/moltbot/moltbot/commit/66eec295b894bce8333886cfbca3b960c57c4946
+  // Agents should use session_status or message timestamps to determine the date/time.
+  // Related: https://github.com/moltbot/moltbot/issues/1897
+  //          https://github.com/moltbot/moltbot/issues/3658
+  it("does NOT include a date or time in the system prompt (cache stability)", () => {
+    const prompt = buildAgentSystemPrompt({
+      workspaceDir: "/tmp/clawd",
+      userTimezone: "America/Chicago",
+      userTime: "Monday, January 5th, 2026 — 3:26 PM",
+      userTimeFormat: "12",
+    });
+
+    // The prompt should contain the timezone but NOT the formatted date/time string.
+    // This is intentional for prompt cache stability — the date/time was removed in
+    // commit 66eec295b. If you're here because you want to add it back, please see
+    // https://github.com/moltbot/moltbot/issues/3658 for the preferred approach:
+    // gateway-level timestamp injection into messages, not the system prompt.
+    expect(prompt).toContain("Time zone: America/Chicago");
+    expect(prompt).not.toContain("Monday, January 5th, 2026");
+    expect(prompt).not.toContain("3:26 PM");
+    expect(prompt).not.toContain("15:26");
+  });
+
   it("includes model alias guidance when aliases are provided", () => {
     const prompt = buildAgentSystemPrompt({
       workspaceDir: "/tmp/clawd",

src/agents/system-prompt.ts

@@ -51,7 +51,12 @@ function buildUserIdentitySection(ownerLine: string | undefined, isMinimal: bool
 
 function buildTimeSection(params: { userTimezone?: string }) {
   if (!params.userTimezone) return [];
-  return ["## Current Date & Time", `Time zone: ${params.userTimezone}`, ""];
+  return [
+    "## Current Date & Time",
+    `Time zone: ${params.userTimezone}`,
+    "If you need the current date, time, or day of week, use the session_status tool.",
+    "",
+  ];
 }
 
 function buildReplyTagsSection(isMinimal: boolean) {