Look at your code a bit closer:

You are adding a menu item, in every iteration, using the exact same key, 'agi'. In the end, your $items array holds only one menu item, for the last language returned by the language_list() function, apparently Turkish.

Hope this helps!

P.S.: Below is a rewrite of your code, without the need for a loop. This implies activating the "Content Translation" module from core. Especially for the 'title' and 'title callback' properties, the documentation is very clear about how to use them in a multilingual setting

"title": Required. The untranslated title of the menu item. "title callback": Function to generate the title; defaults to t(). If you require only the raw string to be output, set this to FALSE.

function suweb_agi_menu() {
  $items = [];
  $items['agi'] = [
    'title' => 'AGİ (Family Status Declaration)',
    'page callback' => 'drupal_get_form',
    'page arguments' => ['suweb_agi_form'],
    'access arguments' => ['access content'],
    'menu_name' => 'menu-sol-menu'
  ];
  return $items;
}

The following code does what you seem to need (screenshots attached). The following modules need to be activated:

• i18n_menu (part of the i18n)

Further configuration:

• I added a new language (tr) and set language detection to "Determine the language from the URL (Path prefix or domain)."

• I added a new menu with machine name (menu-sol-menu) and set the translation mode to "Translate and Localize". Also added the new menu as a block to the header region of the theme.

• Added the following code in a custom module and activated it.

   function agi_menu() {
     $items = [];
     $items['agi'] = [
       'title' => 'AGI (Family Status Declaration)',
       'page callback' => 'drupal_get_form',
       'page arguments' => ['node_form'],
       'access arguments' => ['access content'],
       'menu_name' => 'menu-sol-menu'
     ];
     return $items;
   }
  

I visited the menu admin page and saw that a new menu item was added:

I checked the language option for that new menu item, it was set to neutral.

I visited the home page of my drupal instance and checked that the menu item appears, for both english (default language) and turkish, using the URL to define the current language.

Finally, I looked in the translate interface for the title of the menu item.

Conclusion: The provided code with the described configuration works as expected by the OP.

Good luck!

N.B.: Especially for the 'title' and 'title callback' properties, the documentation is very clear about how to use them in a multilingual setting

"title": Required. The untranslated title of the menu item. "title callback": Function to generate the title; defaults to t(). If you require only the raw string to be output, set this to FALSE.

Look at your code a bit closer:

You are adding a menu item, in every iteration, using the exact same key, 'agi'. In the end, your $items array holds only one menu item, for the last language returned by the language_list() function, apparently Turkish.

Hope this helps!

Look at your code a bit closer:

You are adding a menu item, in every iteration, using the exact same key, 'agi'. In the end, your $items array holds only one menu item, for the last language returned by the language_list() function, apparently Turkish.

Hope this helps!

P.S.: Below is a rewrite of your code, without the need for a loop. This implies activating the "Content Translation" module from core. Especially for the 'title' and 'title callback' properties, the documentation is very clear about how to use them in a multilingual setting

"title": Required. The untranslated title of the menu item. "title callback": Function to generate the title; defaults to t(). If you require only the raw string to be output, set this to FALSE.

function suweb_agi_menu() {
  $items = [];
  $items['agi'] = [
    'title' => 'AGİ (Family Status Declaration)',
    'page callback' => 'drupal_get_form',
    'page arguments' => ['suweb_agi_form'],
    'access arguments' => ['access content'],
    'menu_name' => 'menu-sol-menu'
  ];
  return $items;
}