Cherry Pick: [LYN-7463] Fix insert streaming request failure (#5604) (#5622)

* Fix race condition where asset would finish loading and another request would start before the streamer request could be cleared

Signed-off-by: amzn-mike <80125227+amzn-mike@users.noreply.github.com>

* Re-enable disabled test which was failing for the same reason.

Fix test timeout which was way too long.
Reduce test iterations to keep test time safely under 5 seconds.

Signed-off-by: amzn-mike <80125227+amzn-mike@users.noreply.github.com>

* Instead of using a mutex, re-order the statements to remove the streamer request first

Signed-off-by: amzn-mike <80125227+amzn-mike@users.noreply.github.com>
(cherry picked from commit 0cea59d669)
Signed-off-by: amzn-mike <80125227+amzn-mike@users.noreply.github.com>

Code/Framework/AzCore/AzCore/Asset/AssetManager.cpp

@@ -1677,9 +1677,13 @@ namespace AZ
                 // they will trigger a ReleaseAsset call sometime after the AssetManager has begun to shut down, which can lead to
                 // race conditions.
 
+                // Make sure the streamer request is removed first before the asset is released
+                // If the asset is released first it could lead to a race condition where another thread starts loading the asset
+                // again and attempts to add a new streamer request with the same ID before the old one has been removed, causing
+                // that load request to fail
+                RemoveActiveStreamerRequest(assetId);
                 weakAsset = {};
                 loadingAsset.Reset();
-                RemoveActiveStreamerRequest(assetId);
             };
 
             auto&& [deadline, priority] = GetEffectiveDeadlineAndPriority(*handler, asset.GetType(), loadParams);