feat(version): add stale binary detection with startup warning

Add detection for when the installed gt binary is out of date with the
source repository. This helps catch issues where commands fail mysteriously
because the installed binary doesn't have recent fixes.

Changes:
- Add internal/version package with stale binary detection logic
- Add startup warning in PersistentPreRunE when binary is stale
- Add gt doctor check for stale-binary
- Use prefix matching for commit comparison (handles short vs full hash)

The warning is non-blocking and only shows once per shell session via
the GT_STALE_WARNED environment variable.

Resolves: gt-ud912

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

internal/cmd/root.go

@@ -9,6 +9,7 @@ import (
 
 	"github.com/spf13/cobra"
 	"github.com/steveyegge/gastown/internal/style"
+	"github.com/steveyegge/gastown/internal/version"
 	"github.com/steveyegge/gastown/internal/workspace"
 )
 
@@ -108,10 +109,52 @@ func checkBeadsDependency(cmd *cobra.Command, args []string) error {
 		return nil
 	}
 
+	// Check for stale binary (warning only, doesn't block)
+	checkStaleBinaryWarning()
+
 	// Check beads version
 	return CheckBeadsVersion()
 }
 
+// staleBinaryWarned tracks if we've already warned about stale binary in this session.
+// We use an environment variable since the binary restarts on each command.
+var staleBinaryWarned = os.Getenv("GT_STALE_WARNED") == "1"
+
+// checkStaleBinaryWarning checks if the installed binary is stale and prints a warning.
+// This is a non-blocking check - errors are silently ignored.
+func checkStaleBinaryWarning() {
+	// Only warn once per shell session
+	if staleBinaryWarned {
+		return
+	}
+
+	repoRoot, err := version.GetRepoRoot()
+	if err != nil {
+		// Can't find repo - silently skip (might be running from non-dev environment)
+		return
+	}
+
+	info := version.CheckStaleBinary(repoRoot)
+	if info.Error != nil {
+		// Check failed - silently skip
+		return
+	}
+
+	if info.IsStale {
+		staleBinaryWarned = true
+		os.Setenv("GT_STALE_WARNED", "1")
+
+		msg := fmt.Sprintf("gt binary is stale (built from %s, repo at %s)",
+			version.ShortCommit(info.BinaryCommit), version.ShortCommit(info.RepoCommit))
+		if info.CommitsBehind > 0 {
+			msg = fmt.Sprintf("gt binary is %d commits behind (built from %s, repo at %s)",
+				info.CommitsBehind, version.ShortCommit(info.BinaryCommit), version.ShortCommit(info.RepoCommit))
+		}
+		fmt.Fprintf(os.Stderr, "%s %s\n", style.WarningPrefix, msg)
+		fmt.Fprintf(os.Stderr, "    %s Run 'gt install' to update\n", style.ArrowPrefix)
+	}
+}
+
 // Execute runs the root command and returns an exit code.
 // The caller (main) should call os.Exit with this code.
 func Execute() int {