How to edit dashboard search posts button texts for my CPT?

When registering the post type you should set the search_items label:

register_post_type(
    'question',
    array(
        // etc.
        'labels' => array(
            // etc.
            'search_items' => 'Search Questions',
        ),
    )
);

You can see the full list of labels that you can set here.

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