Homepage with latest posts does not include current-menu-item

That’s because the current menu classes aren’t applied based on the URL but instead based on the main query.

For the homepage, instead use a homepage link block:

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You can edit it just link any other nav menu item or paragraph by clicking and typing on it directly:

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Hata!: SQLSTATE[HY000] [1045] Access denied for user 'divattrend_liink'@'localhost' (using password: YES)