Fix ShutdownHandler health check errors

- Add safe check for ShutdownHandler process existence
- Handle case where ShutdownHandler might not be started yet
- Prevent GenServer.call errors in health checks
- Use Process.whereis and Process.alive? to verify process state

This fixes Sentry errors about 'no process' when health checks
try to call ShutdownHandler.shutting_down?()

🤖 Generated with [Claude Code](https://claude.ai/code)

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

lib/aprsme_web/plugs/health_check.ex

@@ -47,7 +47,7 @@ defmodule AprsmeWeb.Plugs.HealthCheck do
       health_status == :draining ->
         {:error, "Application is draining connections"}
 
-      Aprsme.ShutdownHandler.shutting_down?() ->
+      shutting_down?() ->
         {:error, "Application is shutting down"}
 
       true ->
@@ -105,4 +105,26 @@ defmodule AprsmeWeb.Plugs.HealthCheck do
   rescue
     _ -> {:error, "PubSub check failed"}
   end
+
+  defp shutting_down? do
+    # Check if ShutdownHandler process exists and is shutting down
+    case Process.whereis(Aprsme.ShutdownHandler) do
+      nil ->
+        # Process doesn't exist, not shutting down
+        false
+
+      pid when is_pid(pid) ->
+        # Process exists, check if alive and call it
+        if Process.alive?(pid) do
+          try do
+            GenServer.call(pid, :shutting_down?, 5000)
+          catch
+            :exit, _ -> false
+            _, _ -> false
+          end
+        else
+          false
+        end
+    end
+  end
 end