Treat StartCall like a reserved callback since it is required

include/grpcpp/impl/codegen/client_callback.h

@@ -270,6 +270,7 @@ class ClientCallbackReaderWriterImpl
     // 2. Any read backlog
     // 3. Recv trailing metadata, on_completion callback
     // 4. Any write backlog
+    // 5. See if the call can finish (if other callbacks were triggered already)
     started_ = true;
 
     start_tag_.Set(call_.call(),
@@ -320,6 +321,7 @@ class ClientCallbackReaderWriterImpl
     if (writes_done_ops_at_start_) {
       call_.PerformOps(&writes_done_ops_);
     }
+    MaybeFinish();
   }
 
   void Read(Response* msg) override {
@@ -412,8 +414,8 @@ class ClientCallbackReaderWriterImpl
   CallbackWithSuccessTag read_tag_;
   bool read_ops_at_start_{false};
 
-  // Minimum of 2 outstanding callbacks to pre-register for start and finish
-  std::atomic_int callbacks_outstanding_{2};
+  // Minimum of 3 callbacks to pre-register for StartCall, start, and finish
+  std::atomic_int callbacks_outstanding_{3};
   bool started_{false};
 };
 
@@ -466,6 +468,7 @@ class ClientCallbackReaderImpl
     // 1. Send initial metadata (unless corked) + recv initial metadata
     // 2. Any backlog
     // 3. Recv trailing metadata, on_completion callback
+    // 4. See if the call can finish (if other callbacks were triggered already)
     started_ = true;
 
     start_tag_.Set(call_.call(),
@@ -497,6 +500,8 @@ class ClientCallbackReaderImpl
     finish_ops_.ClientRecvStatus(context_, &finish_status_);
     finish_ops_.set_core_cq_tag(&finish_tag_);
     call_.PerformOps(&finish_ops_);
+
+    MaybeFinish();
   }
 
   void Read(Response* msg) override {
@@ -540,8 +545,8 @@ class ClientCallbackReaderImpl
   CallbackWithSuccessTag read_tag_;
   bool read_ops_at_start_{false};
 
-  // Minimum of 2 outstanding callbacks to pre-register for start and finish
-  std::atomic_int callbacks_outstanding_{2};
+  // Minimum of 3 callbacks to pre-register for StartCall, start, and finish
+  std::atomic_int callbacks_outstanding_{3};
   bool started_{false};
 };
 
@@ -594,6 +599,7 @@ class ClientCallbackWriterImpl
     // 1. Send initial metadata (unless corked) + recv initial metadata
     // 2. Recv trailing metadata, on_completion callback
     // 3. Any backlog
+    // 4. See if the call can finish (if other callbacks were triggered already)
     started_ = true;
 
     start_tag_.Set(call_.call(),
@@ -633,6 +639,8 @@ class ClientCallbackWriterImpl
     if (writes_done_ops_at_start_) {
       call_.PerformOps(&writes_done_ops_);
     }
+
+    MaybeFinish();
   }
 
   void Write(const Request* msg, WriteOptions options) override {
@@ -714,8 +722,8 @@ class ClientCallbackWriterImpl
   CallbackWithSuccessTag writes_done_tag_;
   bool writes_done_ops_at_start_{false};
 
-  // Minimum of 2 outstanding callbacks to pre-register for start and finish
-  std::atomic_int callbacks_outstanding_{2};
+  // Minimum of 3 callbacks to pre-register for StartCall, start, and finish
+  std::atomic_int callbacks_outstanding_{3};
   bool started_{false};
 };