passing value from custom preprocess theme hook function to a template in drupal 9

Question

Situation: I want to write a proprocess PHP function [theme]_preprocess_example__p1 that adds variables to a page template file example--p1.html.twig but the variable cannot display properly if I inlcude the template to page--front.html.twig.

page--front.html.twig

I added the following code in page--front.html.twig

{% include '@[theme]/directory/example--p1.html.twig' %} 

example--p1.html.twig

this file has one variable {{ text }}. to display the text message.

[theme].theme

I added the following code in [theme].theme

[theme]_preprocess_example__p1(array &$variables, $hook){ 
 $variables['name'] = 'message';
 $variables['text'] = 'example p1 message';
 $variables['data'] = 'm1';
}

but I cannot display text variable to the template example--p1.html.twig when I added include {% include '@[theme]/directory/example--p1.html.twig' %} in page--front.html.twig.

Someone suggest creating all the variables to ExampleController.php and use example.module to define hook_theme() function and function [theme]_preprocess_example__p1() but it is failed to display the variables when I include the template example--p1.html.twig for duplicated code to page--front.html.twig template. How can I solve it?