Can not confirm the issue. In short, tried to associate article or to associate menu items or to associate both is working in 6.1.4 and in 6.2.0. Perhaps I am missing something?

Testing with JBT

• Grafted default Joomla_6.1.4-Stable-Full_Package.zip installation, installed de-DE and fr-FR and multilingual sample data
  • System > Plugin > Language Filer > Item Associations > Yes
• Created articles en-GB "2nd article", de-DE "Zweiter Artikel" and fr-FR "deuxième article" and associate the articles
  • Created menu items en-GB "2nd article", de-DE "Zweiter Artikel" and fr-FR "deuxième article" with single article in using the respective article, the respective language main menu and respective language w/o menu item associations
• Created articles en-GB "3rd article", de-DE "Dritter Artikel" and fr-FR "Article trois" and NOT associate the articles
  • Created menu items en-GB "3rd article"", de-DE "Dritter Artikel" and fr-FR "Article trois" and associate the three menu items
• Created articles and menu items en-GB "4th article", de-DE "Vierter Artikel" and fr-FR "Article quatrième" and menu items and associate articles and menu items
• Created articles en-GB "5th article", de-DE "Fünfter Artikel" and fr-FR "Article cinquième" and repective menu items w/o association of articles and menu items
• Saved instance ZIP and SQL (I can hand-over for simple import in JBT or any other installation)
• With 6.1.4 and after update to 6.2.0 there is the same result
  • The 2nd ... 5th menu entries in the three languages are linked to the articles in there languages
  • Using the language switcher, it is possible to switch between the three associated 2nd, 3rd and 4th articles; 5th article goes to main menu

Thank you very much for taking the time to investigate and test this issue.
As I am using Gridbox on this installation I contacted Balbooa support, and they identified the cause of the problem in the Gridbox system plugin.
They provided a modified version of plugins/system/gridbox/src/Extension/Gridbox.php, in which the initialization logic was moved from the class constructor to the onAfterInitialise event.
I tested this modification on my local Joomla 6.2.0 installation, and I can confirm that the language switcher now works correctly, with menu item associations being properly resolved.
It appears that the issue was caused by an incompatibility between the Gridbox system plugin and Joomla 6.2.0, rather than a bug in Joomla itself.
Thank you again for your help and for the detailed testing.
The issue can now be closed.

Not so good, can you share the code where and what happens? Or is this extension public available?

The Gridbox update of the extension is not yet publicly available.
Balbooa support provided a modified version of the system plugin file:
plugins/system/gridbox/src/Extension/Gridbox.php
In the original version, the plugin initialization was performed directly in the class constructor:

public function __construct($subject, $config)
{
$this->dispatcher = $subject;
parent::__construct($subject, $config);
$app = Factory::getApplication();
// Gridbox initialization...
}

In the corrected version, Balbooa removed this constructor and moved the initialization logic to:

public function onAfterInitialise(): void
{
if (!Factory::getApplication()->isClient('site')) {
return;
}
// Gridbox initialization...
}

I hope this will help.

The Gridbox update of the extension is not yet publicly available but you can find the related post on the balbooa support forum (mentioning a downloadable corrective file) :
https://www.balbooa.com/help/forums/gridbox/problem-with-multi-languages-website-after-joomla-6-2-update

Balbooa support provided a modified version of the system plugin file:
plugins/system/gridbox/src/Extension/Gridbox.php
In the original version, the plugin initialization was performed directly in the class constructor:

public function __construct($subject, $config)
{
$this->dispatcher = $subject;
parent::__construct($subject, $config);
$app = Factory::getApplication();
// Gridbox initialization...
}

In the corrected version, Balbooa removed this constructor and moved the initialization logic to:

public function onAfterInitialise(): void
{
if (!Factory::getApplication()->isClient('site')) {
return;
}
// Gridbox initialization...
}

I hope this will help.

so can you confirm if this is a problem with Joomla core or with the extension

Based on my testing, the issue appears to be related to the Balbooa Gridbox extension rather than Joomla core.
The problem occurred after upgrading from Joomla 6.1.4 to 6.2.0, but Balbooa provided a fix that moves the plugin initialization logic from the class constructor to the onAfterInitialise event.
After applying this fix, the language switcher and menu item associations work correctly again on Joomla 6.2.0.
So I can confirm that the extension-side fix resolves the issue, although I cannot determine whether a change in Joomla 6.2.0 contributed to exposing the incompatibility.

Based on my testing, the issue appears to be related to the Balbooa Gridbox extension rather than Joomla core.
The problem occurred after upgrading from Joomla 6.1.4 to 6.2.0, but Balbooa provided a fix that moves the plugin initialization logic from the class constructor to the onAfterInitialise event.
After applying this fix, the language switcher and menu item associations work correctly again on Joomla 6.2.0.
So I can confirm that the extension-side fix resolves the issue, although I cannot determine whether a change in Joomla 6.2.0 contributed to exposing the incompatibility. Balbooa confirmed that this fix will be included in the next Gridbox update.

thanks for sharing the code, so it's actually a wrong way the extension using the joomla api, you shouldn't do anything in the constructor since we can't guarantee when and if it's called.

I'm closing this issues now. Thanks for the report