[call-v3] Add a hook to deadline filter (#35252)

Still need to figure a better long term strategy here, but this 'works for now'

Closes #35252

COPYBARA_INTEGRATE_REVIEW=https://github.com/grpc/grpc/pull/35252 from ctiller:cg-deadline a413955afc
PiperOrigin-RevId: 588980941

src/core/ext/filters/deadline/deadline_filter.cc

@@ -369,7 +369,17 @@ const grpc_channel_filter grpc_server_deadline_filter = {
       }
       return next_promise_factory(std::move(call_args));
     },
-    /* init_call: */ nullptr,
+    [](grpc_channel_element*, grpc_core::CallSpineInterface* spine) {
+      spine->client_initial_metadata().receiver.InterceptAndMap(
+          [](grpc_core::ClientMetadataHandle md) {
+            auto deadline = md->get(grpc_core::GrpcTimeoutMetadata());
+            if (deadline.has_value()) {
+              grpc_core::GetContext<grpc_core::CallContext>()->UpdateDeadline(
+                  *deadline);
+            }
+            return md;
+          });
+    },
     grpc_channel_next_op,
     sizeof(server_call_data),
     deadline_init_call_elem,