[Tasks] Mark parent as sticky if we use @async (#41334)

Fixes #41324 for 1.7

(cherry picked from commit 75858d7)

base/task.jl

@@ -621,6 +621,12 @@ function enq_work(t::Task)
     # 3. The multiq is full (can be fixed by making it growable).
     if t.sticky || Threads.nthreads() == 1
         if tid == 0
+            # Issue #41324
+            # t.sticky && tid == 0 is a task that needs to be co-scheduled with
+            # the parent task. If the parent (current_task) is not sticky we must
+            # set it to be sticky.
+            # XXX: Ideally we would be able to unset this
+            current_task().sticky = true
             tid = Threads.threadid()
             ccall(:jl_set_task_tid, Cvoid, (Any, Cint), t, tid-1)
         end

test/threads_exec.jl

@@ -840,6 +840,19 @@ fib34666(x) =
     end
 @test fib34666(25) == 75025
 
+# issue #41324
+@testset "Co-schedule" begin
+    parent = Threads.@spawn begin
+        @test current_task().sticky == false
+        child = @async begin end
+        @test current_task().sticky == true
+        @test Threads.threadid() == Threads.threadid(child)
+        wait(child)
+    end
+    wait(parent)
+    @test parent.sticky == true
+end
+
 function jitter_channel(f, k, delay, ntasks, schedule)
     x = Channel(ch -> foreach(i -> put!(ch, i), 1:k), 1)
     y = Channel(k) do ch