How to share specific data contained in repeated fields across multiple pages

Rather than outputting all rows, you can check each row in a loop and only output it if something matches.

In this example, there’s a treatment field within the repeater that is the value of the name of the treatment post. If the two match, output the other values:

$other_page = 89;
$practioners = get_field( 'about_the_practioner' , $other_page );
foreach( $practioners as $practioner ):
    if( get_the_title() == $practioner['treatment'] ):
        echo '<h4>' . $practioner['title'] . '</h4>';
    endif;
endforeach;

As an added bonus, you can create a select field to select the treatment post for each practitioner by dynamically adding the post titles as select field values. See the ACF documentation for the acf_load_field filter. Inside the filter function, you can query for all treatment posts and add each title as a select option.