feat(dev): add systemd timer for beads gate check

Add periodic timer (every 5 min) that runs `bd gate check --type=timer`
across all beads workspaces with running daemons.

This enables self-scheduling molecules - workflows that can set timer
gates to schedule their own future execution (e.g., watchers that scan
Slack every 8 hours).

The timer:
- Only runs on Linux (uses systemd user services)
- Discovers workspaces via `bd daemon list`
- Silently skips if no beads daemons are running

Related: nixos-configs-1rk.2 (Time beads scheduling mechanism)

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

home/roles/development/default.nix

@@ -146,6 +146,46 @@ in
       $DRY_RUN_CMD echo "Claude Code beads integration configured (hooks installed)"
     '';
 
+    # Beads timer gate checker (Linux only - uses systemd)
+    # Runs every 5 minutes to auto-resolve expired timer gates across all beads projects
+    # This enables self-scheduling molecules (watchers, patrols, etc.)
+    systemd.user.services.beads-gate-check = lib.mkIf pkgs.stdenv.isLinux {
+      Unit = {
+        Description = "Check and resolve expired beads timer gates";
+      };
+      Service = {
+        Type = "oneshot";
+        # Check gates in all workspaces that have running daemons
+        ExecStart = pkgs.writeShellScript "beads-gate-check-all" ''
+          # Get list of workspaces from daemon registry
+          workspaces=$(${beadsPackage}/bin/bd daemon list --json 2>/dev/null | ${pkgs.jq}/bin/jq -r '.[].workspace // empty' 2>/dev/null)
+
+          if [ -z "$workspaces" ]; then
+            exit 0  # No beads workspaces, nothing to do
+          fi
+
+          for ws in $workspaces; do
+            if [ -d "$ws" ]; then
+              cd "$ws" && ${beadsPackage}/bin/bd gate check --type=timer --quiet 2>/dev/null || true
+            fi
+          done
+        '';
+      };
+    };
+
+    systemd.user.timers.beads-gate-check = lib.mkIf pkgs.stdenv.isLinux {
+      Unit = {
+        Description = "Periodic beads timer gate check";
+      };
+      Timer = {
+        OnBootSec = "5min";
+        OnUnitActiveSec = "5min";
+      };
+      Install = {
+        WantedBy = [ "timers.target" ];
+      };
+    };
+
     # Note: modules must be imported at top-level home config
   };
 }