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

By itself this is a no-op, but a future change will leverage this to allow fuzzers to inject thread hops into party activations (a technique that has helped find multiple log lived bugs in the past 24 hours)

Closes #38139

COPYBARA_INTEGRATE_REVIEW=https://github.com/grpc/grpc/pull/38139 from ctiller:flake-fightas-30 e19a1af694
PiperOrigin-RevId: 697620027

src/core/lib/promise/party.cc

@@ -29,11 +29,6 @@
 #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 {
 
 ///////////////////////////////////////////////////////////////////////////////
@@ -193,16 +188,13 @@ void Party::ForceImmediateRepoll(WakeupMask mask) {
 
 void Party::RunLockedAndUnref(Party* party, uint64_t prev_state) {
   GRPC_LATENT_SEE_PARENT_SCOPE("Party::RunLocked");
-#ifdef GRPC_MAXIMIZE_THREADYNESS
-  Thread thd(
-      "RunParty",
-      [party, prev_state]() {
+#if defined(GRPC_MAXIMIZE_THREADYNESS)
+  party->arena_->GetContext<grpc_event_engine::experimental::EventEngine>()
+      ->Run([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;