Split MAX bot loops and make chats cache-first

server/QMax.Api/Services/MaxOutboxService.cs

@@ -21,8 +21,12 @@ public sealed class MaxOutboxService(
 
     public async Task<int> ProcessOnceAsync(CancellationToken cancellationToken)
     {
-        var processed = 0;
+        var processed = await ProcessPendingMessagesOnceAsync(cancellationToken);
+        return processed + await ProcessPendingChatActionsOnceAsync(cancellationToken);
+    }
 
+    public async Task<int> ProcessPendingMessagesOnceAsync(CancellationToken cancellationToken)
+    {
         var candidates = await db.Messages
             .Include(message => message.Chat)
             .Include(message => message.Attachments)
@@ -41,6 +45,7 @@ public sealed class MaxOutboxService(
             .Take(10)
             .ToArray();
 
+        var processed = 0;
         foreach (var message in pending)
         {
             cancellationToken.ThrowIfCancellationRequested();
@@ -50,10 +55,10 @@ public sealed class MaxOutboxService(
             }
         }
 
-        return processed + await ProcessPendingChatActionsAsync(cancellationToken);
+        return processed;
     }
 
-    private async Task<int> ProcessPendingChatActionsAsync(CancellationToken cancellationToken)
+    public async Task<int> ProcessPendingChatActionsOnceAsync(CancellationToken cancellationToken)
     {
         var now = DateTimeOffset.UtcNow;
         var pending = await db.Chats