Steps to reproduce the issue

1. Create a tag "PC".
2. Create one article and tag it to "PC".
3. Create a menu item type "Tagged Items" and set tag to "PC" and Content Type do "Article".
4. Create a menu item type "Compact List of Tagged Items" and set tag to "PC" and Content Type do "Article".
5. Turn SEF off in the Joomla global settings. Just for testing, but it does not work even with SEF on.

In my case I have Itemid 120 for "Tagged Items" and Itemid 123 for "Compact List of Tagged Items"

I made a simple system plugin and used "onBeforeCompileHead" and "onContentPrepareForm" events to show site routing of the same "Tagged Items" URL on Front-end and Back-end.

public function onBeforeCompileHead()
{
	$doc = $this->app->getDocument();
	if (!($this->app->isClient('site')) || ($doc->getType() != 'html')) return;
	$testURL = 'index.php?option=com_tags&view=tag&id[0]=2&types[0]=1&Itemid=120';
	echo 'Routed URL: '.ROUTE::link('site', $testURL);
}

public function onContentPrepareForm(Form $form, $data)
{
	$doc = $this->app->getDocument();
        if (!($this->app->isClient('administrator')) || ($doc->getType() != 'html')) return;
        $testURL = 'index.php?option=com_tags&view=tag&id[0]=2&types[0]=1&Itemid=120';
        $noticeMsg = 'Routed URL: '.ROUTE::link('site', $testURL);
	$this->app->enqueueMessage($noticeMsg, 'notice');
}

Expected result

For the same URL, ROUTE::link('site', $testURL) must returns same results in Front-end and Back-end.

Actual result

In my test ROUTE::link('site', $testURL) returns

/joomla5/index.php?option=com_tags&view=tag&id[0]=2&types[0]=1&Itemid=120

in Back-end and

/joomla5/index.php?option=com_tags&view=tag&id[0]=2&types[0]=1&Itemid=123

in Front-end.
As you can see, Front-end results link to the wrong Itemid (Compact List of Tagged Items)

System information (as much as possible)

Ubuntu 22.04.4
PHP 8.1.2
MariaDB 10.6.16
Apache/2.4.52
Joomla! 5.0.3 Stable [ Kuboresha ]
Joomla Backward Compatibility Plugin Disabled

Additional comments