Instantiating and Deleting a prefab requires the user to save the level twice

[srikappa-amzn]

Describe the bug
Instantiating and Deleting a prefab requires the user to save the level twice

Steps to reproduce
Steps to reproduce the behavior:

1. Open any level
2. Instantiate a new prefab
3. Hit Ctrl+S or file->save. Notice that the level is still marked dirty
4. Hit Ctrl+S again. Notice that it is saved now.
5. Repeat the same steps but with deleting the prefab instead of instantiating it.

Expected behavior
Level gets saved correctly on the first save.

Actual behavior
Level is still marked dirty after hitting ctrl+s for the first time.

Found in Branch
stabilization/2210 and development

[jckand]

If fix ends up to be too risky for stabilization, we can add a release note for this issue instead.

[forkercat]

Did some closer look. Similar to #11452 (multiple Ctrl+S for create-entity).

For instantiate-prefab workflow, I suggest putting (1) to stabilization and then merge back to development. (2) can be added to development later.

1. Add prefab undo cache update (I verified this should be enough fix the issue)
2. Add the missing parent DOM update (this is needed as we're removing prefab undo cache and depend on DOM in template)

For delete workflow, the workflow was reworked in development (#11699). I verified the issue no longer occurs in development now. For the old workflow in stabilization, I don't think there is a temp fix we can go ahead at this time because it does not know parent entity info during deletion, which is unlike the new workflow.

1. We can either merge the new workflow to stabilization. Or
2. Keep unchanged for this release.

[forkercat]

[ Update 9/22 ]

1. For instantiate-prefab, verified fixed in both development and stabilization.
2. For delete-prefab, verified fixed in development after the rework commit for deletion. But that was before stab cut-off and it is a bit risky to cherry-pick it into stab at this time.