get_template_part() not working with Advanced Custom Fields plugin

as you use multiple $testimonials i suppose those are group values.

then you need to use get_sub_field() in place of get_field()

so it should look like 

$term = get_queried_object();
$testimonials = get_sub_field('testimonials',$term);
echo $testimonials['small_title'];
echo $testimonials['main_title'];
echo $testimonials['description'];

Please refer to ACF documentation when you use non classical fields.
https://www.advancedcustomfields.com/resources/group/

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