Revert "[party] use ee for max threadyness (#38139)"

This reverts commit 3cc611c7df.

src/core/lib/promise/party.cc

@@ -29,6 +29,11 @@
 #include "src/core/util/latent_see.h"
 #include "src/core/util/sync.h"
 
+#ifdef GRPC_MAXIMIZE_THREADYNESS
+#include "src/core/lib/iomgr/exec_ctx.h"  // IWYU pragma: keep
+#include "src/core/util/thd.h"            // IWYU pragma: keep
+#endif
+
 namespace grpc_core {
 
 ///////////////////////////////////////////////////////////////////////////////
@@ -188,13 +193,16 @@ void Party::ForceImmediateRepoll(WakeupMask mask) {
 
 void Party::RunLockedAndUnref(Party* party, uint64_t prev_state) {
   GRPC_LATENT_SEE_PARENT_SCOPE("Party::RunLocked");
-#if defined(GRPC_MAXIMIZE_THREADYNESS)
-  party->arena_->GetContext<grpc_event_engine::experimental::EventEngine>()
-      ->Run([party, prev_state]() {
+#ifdef GRPC_MAXIMIZE_THREADYNESS
+  Thread thd(
+      "RunParty",
+      [party, prev_state]() {
         ApplicationCallbackExecCtx app_exec_ctx;
         ExecCtx exec_ctx;
         party->RunPartyAndUnref(prev_state);
-      });
+      },
+      nullptr, Thread::Options().set_joinable(false));
+  thd.Start();
 #else
   struct RunState;
   static thread_local RunState* g_run_state = nullptr;