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@mpurkaya76

Are you using an original classic theme?
Currently, the target="_blank" is added based on class names like .post-xxx.
If your post element includes post_class();, the .post-xxx class will be automatically output.
If not, please add it in your theme manually.
In the case of block themes, .post-xxx is automatically added by blocks like the Query Loop block, so it should work without any issues.

Even if you are using get_permalink(), the link will open in a new tab as long as post_class() is properly applied.

Ex)

<div <?php post_class();?>>
<a href="<?php echo get_permalink()?>">Link Text</a>
</div>

Therefore, the issue occurs because the theme does not include post_class() (or .post-xxx class).

There is nothing that can be done on the plugin side.

Please request the theme author to add it.