[backport] Fix inplace predict with fallback when base margin is used. (#9536) (#9548)

- Copy meta info from proxy DMatrix.
- Use `std::call_once` to emit less warnings.

src/gbm/gbtree.cc

@@ -85,25 +85,6 @@ bool UpdatersMatched(std::vector<std::string> updater_seq,
                       return name == up->Name();
                     });
 }
-
-void MismatchedDevices(Context const* booster, Context const* data) {
-  bool thread_local static logged{false};
-  if (logged) {
-    return;
-  }
-  LOG(WARNING) << "Falling back to prediction using DMatrix due to mismatched devices. This might "
-                  "lead to higher memory usage and slower performance. XGBoost is running on: "
-               << booster->DeviceName() << ", while the input data is on: " << data->DeviceName()
-               << ".\n"
-               << R"(Potential solutions:
-- Use a data structure that matches the device ordinal in the booster.
-- Set the device for booster before call to inplace_predict.
-
-This warning will only be shown once for each thread. Subsequent warnings made by the
-current thread will be suppressed.
-)";
-  logged = true;
-}
 }  // namespace
 
 void GBTree::Configure(Args const& cfg) {
@@ -554,7 +535,7 @@ void GBTree::InplacePredict(std::shared_ptr<DMatrix> p_m, float missing,
   auto [tree_begin, tree_end] = detail::LayerToTree(model_, layer_begin, layer_end);
   CHECK_LE(tree_end, model_.trees.size()) << "Invalid number of trees.";
   if (p_m->Ctx()->Device() != this->ctx_->Device()) {
-    MismatchedDevices(this->ctx_, p_m->Ctx());
+    error::MismatchedDevices(this->ctx_, p_m->Ctx());
     CHECK_EQ(out_preds->version, 0);
     auto proxy = std::dynamic_pointer_cast<data::DMatrixProxy>(p_m);
     CHECK(proxy) << error::InplacePredictProxy();
@@ -807,7 +788,7 @@ class Dart : public GBTree {
     auto n_groups = model_.learner_model_param->num_output_group;
 
     if (ctx_->Device() != p_fmat->Ctx()->Device()) {
-      MismatchedDevices(ctx_, p_fmat->Ctx());
+      error::MismatchedDevices(ctx_, p_fmat->Ctx());
       auto proxy = std::dynamic_pointer_cast<data::DMatrixProxy>(p_fmat);
       CHECK(proxy) << error::InplacePredictProxy();
       auto p_fmat = data::CreateDMatrixFromProxy(ctx_, proxy, missing);