typo3 - Where to influence in which languages an extbase record can be translated?

Question

In a custom built TYPO3 extension, records are only available in language -1 in the backend. That was specified as such, but should now be changed so records can be translated.

Something is missing. I thought this would be in TCA, but the definitions look quite normal:

'columns' => [
    'sys_language_uid' => [
      'exclude' => true,
      'label' => 'LLL:EXT:lang/locallang_general.xlf:LGL.language',
      'config' => [
        'type' => 'select',
        'renderType' => 'selectSingle',
        'special' => 'languages',
        'items' => [
          [
            'LLL:EXT:lang/locallang_general.xlf:LGL.allLanguages',
            -1,
            'flags-multiple'
          ]
        ],
        'default' => 0,
      ],
    ],
    'l10n_parent' => [
      'displayCond' => 'FIELD:sys_language_uid:>:0',
      'exclude' => true,
      'label' => 'LLL:EXT:lang/locallang_general.xlf:LGL.l18n_parent',
      'config' => [
        'type' => 'select',
        'renderType' => 'selectSingle',
        'items' => [
          ['', 0],
        ],
        'foreign_table' => 'tx_myext_domain_model_item',
        'foreign_table_where' => 'AND tx_myext_domain_model_item.pid=###CURRENT_PID### AND tx_myext_domain_model_item.sys_language_uid IN (-1,0)',
      ],
    ],

Also, when I change TCA, for example change config as such:

'config' => array(
                'type' => 'select',
                'renderType' => 'selectSingle',
                'foreign_table' => 'sys_language',
                'foreign_table_where' => 'ORDER BY sys_language.title',
                'items' => array(
                    array('LLL:EXT:lang/locallang_general.xlf:LGL.allLanguages', -1),
                    array('LLL:EXT:lang/locallang_general.xlf:LGL.default_value', 0)
                ),
            ),

It's still the same: only language -1 (ALL) is selectable.

Of course, the sysfolder those records are on is translated in multiple languages. Also, the columns for sys_language_uid, l10n_parent and l10n_diffsource are present in the database.

• Are the other languages maybe disabled somewhere? Where else could I look?
• Or which element could be missing else to make records translateable?

Thanks for any hint.