When I create a new administrator menu and make changes - the quicklink (+) icon disappears on:

• categories
• site modules
• main menu

It was fixed for articles in 27885.

Steps to reproduce the issue

1. Create a new Administrator Menu - use the default menu preset
2. Open the Menu
3. Edit Content > Categories or Content > Site Modules or Menus > Main Menu etc.
4. After saving the quick task icon, and URL disappears.

Youtube Steps (Fresh Install):
https://youtu.be/tAVDoDrv-Vk

Issue 2
Export your menu, and its missing:

• quicktask
• quicktask-title
• class?

If you add quicktask via MYSQL - the quicktask is missing on export.

####Expected result

1. Quick Icon should remain.
2. Output should include quicktask like defauly.xml does:

<menuitem
			title="MOD_MENU_EXTENSIONS_MODULE_MANAGER_SITE"
			quicktask-title="COM_CONTENT_MENUS_NEW_SITE_MODULE"
			type="component"
			element="com_modules"
			link="index.php?option=com_modules&amp;view=modules&amp;client_id=0"
			quicktask="index.php?option=com_modules&amp;view=select&amp;client_id=0"
		/>

Actual result

1. Quick Icon Disappears
   
2. Output excludes quicktask:

<menuitem 
type="component" 
title="MOD_MENU_EXTENSIONS_MODULE_MANAGER_SITE" 
link="index.php?option=com_modules&amp;view=modules&amp;client_id=0" 
element="com_modules" class=" "/>

System information (as much as possible)

Joomla 4.4.3

Additional comments

Could the system URL link include the quicktask info?