Make merge_agent_work async to avoid MCP 60-second tool timeout

The merge pipeline (squash merge + quality gates) takes well over 60
seconds. Claude Code's MCP HTTP transport times out at 60s, causing
"completed with no output" — the mergemaster retries fruitlessly.

merge_agent_work now starts the pipeline as a background task and
returns immediately. A new get_merge_status tool lets the mergemaster
poll until the job reaches a terminal state. Also adds a double-start
guard so concurrent calls for the same story are rejected.

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

server/src/agents/merge.rs

@@ -1,5 +1,6 @@
 use std::path::Path;
 use std::process::Command;
+use std::sync::Mutex;
 
 use serde::Serialize;
 
@@ -7,6 +8,29 @@ use crate::config::ProjectConfig;
 
 use super::gates::run_project_tests;
 
+/// Global lock ensuring only one squash-merge runs at a time.
+///
+/// The merge pipeline uses a shared `.story_kit/merge_workspace` directory and
+/// temporary `merge-queue/{story_id}` branches.  If two merges run concurrently,
+/// the second call's initial cleanup destroys the first call's branch mid-flight,
+/// causing `git cherry-pick merge-queue/…` to fail with "bad revision".
+static MERGE_LOCK: Mutex<()> = Mutex::new(());
+
+/// Status of an async merge job.
+#[derive(Debug, Clone, Serialize)]
+pub enum MergeJobStatus {
+    Running,
+    Completed(MergeReport),
+    Failed(String),
+}
+
+/// Tracks a background merge job started by `merge_agent_work`.
+#[derive(Debug, Clone, Serialize)]
+pub struct MergeJob {
+    pub story_id: String,
+    pub status: MergeJobStatus,
+}
+
 /// Result of a mergemaster merge operation.
 #[derive(Debug, Serialize, Clone)]
 pub struct MergeReport {
@@ -57,6 +81,11 @@ pub(crate) fn run_squash_merge(
     branch: &str,
     story_id: &str,
 ) -> Result<SquashMergeResult, String> {
+    // Acquire the merge lock so concurrent calls don't clobber each other.
+    let _lock = MERGE_LOCK
+        .lock()
+        .map_err(|e| format!("Merge lock poisoned: {e}"))?;
+
     let mut all_output = String::new();
     let merge_branch = format!("merge-queue/{story_id}");
     let merge_wt_path = project_root