Fix "context canceled" with partial

Make sure the context used for timeouts isn't created based on the incoming
context, as we have cases where this can cancel the context prematurely.

Fixes #10789

lazy/init_test.go

@@ -126,12 +126,6 @@ func TestInitAddWithTimeoutTimeout(t *testing.T) {
 
 	init := New().AddWithTimeout(100*time.Millisecond, func(ctx context.Context) (any, error) {
 		time.Sleep(500 * time.Millisecond)
-		select {
-		case <-ctx.Done():
-			return nil, nil
-		default:
-		}
-		t.Fatal("slept")
 		return nil, nil
 	})