index.php isn’t front page but shows as it is

is_home() and is_front_page() can be a bit confusing, they’re both true on the same page if your front page is the posts page, but in your case with a static front page, is_home() is true on your blog page, and is_front_page() is true on your static front page.

From Conditional Tags:

is_home(): When the main blog page is being displayed. This is the page which shows the time based blog content of your site, so if you’ve set a static Page for the Front Page (see below), then this will only be true on the Page which you set as the “Posts page” in Administration > Settings > Reading.

So if you want your link everywhere but the front page, change it to if( !is_front_page() )

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