How to change search result icon based on the content category

I think you could do it with a little JavaScript, conceptually:

- Each search result has a page link where it leads to the topic, the URL of the link contains the board id, which you probably can use to distinguish between external and internal TKB?

- If so, you can loop trough all search results, check the page-link for each result and add a CSS class in the appropriate place to target the :before element (that is the icon)

something like this (entirely untested) could do it:

jQuery('.lia-message-subject-wrapper .page-link').each(function() {
    var $link = jQuery(this);

    // for internal links
    if ( $link.is('[href*="<your.internal.tkb.board.id>"]') ) {
        $link
            .parents('.lia-quilt-message-search-item')
            .find('.lia-component-discussion-style-icon .lia-fa-icon')
            .addClass('is--internal');
    }

    // for external links, of course handling one type of links is enough,
    // you just style one differently (most likely) and leave to other one alone, your choice!
    if ( $link.is('[href*="<your.external.tkb.board.id>"]') ) {
        $link
            .parents('.lia-quilt-message-search-item')
            .find('.lia-component-discussion-style-icon .lia-fa-icon')
            .addClass('is--external');
    }

    // now you need to add CSS styles accordingly to change the color of your icon, e.g. this would do it
    /*
    .SearchPage .lia-fa-icon.is--internal:before {
        color: red;
    }
    .SearchPage .lia-fa-icon.is--external:before {
        color: green;
    }
    */

});

does that work for you?