Hold on with the PR as I might found an issue with this.

Ok, it should be fine now. There was a missing root option in com_categories when used in com_categories itself. Now there is just a layout option for that thing if any of the extensions need a root option in the category batch pop-up. Also, in the batch pop-up I change JHtml to JLayout instead cause modifying JHtml function felt wrong.

This does not work here. I don't get the language tag between parenthesis after the cat name.
Please add a screenshot of what you get (or want to get) after this PR.

@infograf768 Give me few hours. While adding missing "Add to root" option I removed the fix I made in the first place :D Need to find a solution to reconcile both of the fixes

You are failing because the change is very simple and only concerns one file:

diff --git a/libraries/cms/html/category.php b/libraries/cms/html/category.php
index 413c246..0d7b76d 100644
--- a/libraries/cms/html/category.php
+++ b/libraries/cms/html/category.php
@@ -155,5 +155,5 @@
 			$db = JFactory::getDbo();
 			$query = $db->getQuery(true)
-				->select('a.id, a.title, a.level, a.parent_id')
+				->select('a.id, a.title, a.level, a.parent_id, a.language')
 				->from('#__categories AS a')
 				->where('a.parent_id > 0');
@@ -192,4 +192,10 @@
 				$repeat = ($item->level - 1 >= 0) ? $item->level - 1 : 0;
 				$item->title = str_repeat('- ', $repeat) . $item->title;
+
+				if ($item->language !== '*')
+				{
+					$item->title .= ' (' . $item->language . ')';
+				}
+
 				static::$items[$hash][] = JHtml::_('select.option', $item->id, $item->title);
 			}

In the screen shot below the only change is adding (xx-XX) after the name as I already added in some of the categories names the lang tag.

I can make new PR and delete this one.

Yeah, that was the missing part to keep both changes. But now I'm interested if there is a point to keep both category.options and category.categories cause they both seems to do the same. but with or without root item.

I would not merge this PR.
The change I proposed is enough. Not necessary to modify other files.
If you want to refactor totally this feature, please propose it for 4.0.

@infograf768 So do it your way.

I created the PR #29003

I suggest you make a specific PR for the rest vs J4

@artur-stepien
I will make specific PR for J4 using your code adapted to J4 as layout helpers are used for all batch and there are no specific differenciation between category.categories and category.options

@infograf768 Thanks.

Can be tested here
#29053