[e2e] Fix failure in thready_tsan for cancel_before_invoke with v3 (#36955)

We should only start a call if we're going to use that call (which means not if the call is already cancelled!)

Closes #36955

COPYBARA_INTEGRATE_REVIEW=https://github.com/grpc/grpc/pull/36955 from ctiller:flakezzzz 2368338bf6
PiperOrigin-RevId: 644171653

src/core/lib/surface/client_call.cc

@@ -231,13 +231,15 @@ void ClientCall::StartCall(const grpc_op& send_initial_metadata_op) {
   auto call = MakeCallPair(std::move(send_initial_metadata_), event_engine(),
                            arena()->Ref());
   started_call_initiator_ = std::move(call.initiator);
-  call_destination_->StartCall(std::move(call.handler));
   while (true) {
+    GRPC_TRACE_LOG(call, INFO)
+        << DebugTag() << "StartCall " << GRPC_DUMP_ARGS(cur_state);
     switch (cur_state) {
       case kUnstarted:
         if (call_state_.compare_exchange_strong(cur_state, kStarted,
                                                 std::memory_order_acq_rel,
                                                 std::memory_order_acquire)) {
+          call_destination_->StartCall(std::move(call.handler));
           return;
         }
         break;
@@ -249,6 +251,7 @@ void ClientCall::StartCall(const grpc_op& send_initial_metadata_op) {
         if (call_state_.compare_exchange_strong(cur_state, kStarted,
                                                 std::memory_order_acq_rel,
                                                 std::memory_order_acquire)) {
+          call_destination_->StartCall(std::move(call.handler));
           auto unordered_start = reinterpret_cast<UnorderedStart*>(cur_state);
           while (unordered_start->next != nullptr) {
             unordered_start->start_pending_batch();