Confirmed... the order of the submenus doesn't change in frontend and it switch back to the previous order in the backend, when you load the backend again..

works in 4.1.2
fails in 4.1.3

works in 4.1.2 fails in 4.1.3
As you said, there is no problem in 4.1.2.

@dgrammatiko Look like it causes by your PR #36353 . From my quick look, we are passing more data for order[] variable than needed.

Before your PR, we only submit cid[] ad order[] from affected rows (within the same level) but after your PR, data from all hidden order[] are posted in the request and it causes this error.

One solution would be delete order[] (and maybe cid[]) from formData. That should solve this issue but I'm unsure if it would cause any side affect. Could you please take a look?

Just revert that PR. That PR was wrong but some devs were insisting. Also it hasn't properly tested. If it had it would never been merged. Multiplying the wrongs won't produce a right...

So what's different in the menu then in modules. maybe the tree structure? does it fail with categories too?

So what's different in the menu then in modules

The sorting has 2 modes: flat and nested. I guess nobody tested the nested thing. Anyways that PR WAS wrongly trying to satisfy requirements that the CMS will never encounter. There were 2 thumbs down, the one was from me, the author of the PR and there's some more context in the issue that pushed me to open that PR...

@dgrammatiko If your PR is so wrong, why not just close it instead of thumbs down? Besides that I wonder what was changed in 4.1.3 that causes to break it.

The sorting has 2 modes: flat and nested. I guess nobody tested the nested thing

modules is only flat hence the problem did not occur.

Besides that I wonder what was changed in 4.1.3 that causes to break it.

@joomdonation explained few posts above what caused the break

If your PR is so wrong, why not just close it instead of thumbs down?

I was asked not to close it, (there's more here but not for public consumption, the issue has some leads)

Besides that I wonder what was changed in 4.1.3 that causes to break it.

@roland-d The PR was merged 19 days ago and so released with 4.1.3 and do not in 4.1.2 yet. So the PR was the breaking change, nothing else. It’s like @dgrammatiko said: The PR has not been tested with the nested option, possibly because the testing instructions did not include that.

PR #37781 should fix this issue, so I'm closing the issue. If anyone has this issue on your live site, please get this zip file, unzip it, upload received files to media/system/js folder on your site, then clear browser cache (press Ctrl + F5) and the issue will be sorted.
draggable.zip

@joomdonation
I did a fresh install and tried again, the problem persists for me.

@joomlaphp After uploading the modified JS files, please make sure you clear browser cache (press Ctrl + F5) before checking it again. Maybe it is not working because your browser is still caching the old js files?

Sorry I commented on the closed related issue: #37786
I applied the provided patch with clean cache and there's a still a slight issue: drag the same item 3 times and and it will skip saving the third one. It's evident with both modules and menus.