Slack: implement replyToMode threading for tool path

- Add shared hasRepliedRef state between auto-reply and tool paths
- Extract buildSlackThreadingContext helper in agent-runner.ts
- Extract resolveThreadTsFromContext helper in slack-actions.ts
- Update docs with clear replyToMode table (off/first/all)
- Add tests for first mode behavior across multiple messages

src/agents/pi-embedded-runner.ts

@@ -868,6 +868,7 @@ export async function compactEmbeddedPiSession(params: {
           sessionKey: params.sessionKey ?? params.sessionId,
           agentDir,
           config: params.config,
+          // No currentChannelId/currentThreadTs for compaction - not in message context
         });
         const machineName = await getMachineDisplayName();
         const runtimeProvider = normalizeMessageProvider(
@@ -999,6 +1000,14 @@ export async function runEmbeddedPiAgent(params: {
   sessionKey?: string;
   messageProvider?: string;
   agentAccountId?: string;
+  /** Current channel ID for auto-threading (Slack). */
+  currentChannelId?: string;
+  /** Current thread timestamp for auto-threading (Slack). */
+  currentThreadTs?: string;
+  /** Reply-to mode for Slack auto-threading. */
+  replyToMode?: "off" | "first" | "all";
+  /** Mutable ref to track if a reply was sent (for "first" mode). */
+  hasRepliedRef?: { value: boolean };
   sessionFile: string;
   workspaceDir: string;
   agentDir?: string;
@@ -1200,6 +1209,10 @@ export async function runEmbeddedPiAgent(params: {
             sessionKey: params.sessionKey ?? params.sessionId,
             agentDir,
             config: params.config,
+            currentChannelId: params.currentChannelId,
+            currentThreadTs: params.currentThreadTs,
+            replyToMode: params.replyToMode,
+            hasRepliedRef: params.hasRepliedRef,
           });
           const machineName = await getMachineDisplayName();
           const runtimeInfo = {