How does WP detect format type (and can I make use of this)?

This functionality appears to be exclusively a feature of the block editor. It's not especially clever either. All it does is check that if the post has 1 or 2 blocks (and no more), and then maps the first block against a list of appropriate post formats, like so:

switch ( name ) {
    case 'core/image':
        return 'image';
    case 'core/quote':
    case 'core/pullquote':
        return 'quote';
    case 'core/gallery':
        return 'gallery';
    case 'core/video':
    case 'core-embed/youtube':
    case 'core-embed/vimeo':
        return 'video';
    case 'core/audio':
    case 'core-embed/spotify':
    case 'core-embed/soundcloud':
        return 'audio';
}

This is part of the getSuggestedPostFormat() selector function that's part of the core/editor data store. You can see the full source in the Gutenberg repository here. This seems like a good overview of what the data stores in the block editor are.

To use this function in JS in the editor you could use:

wp.data.select('core/editor').getSuggestedPostFormat();

The logic is simple enough that it's trivial to implement in PHP with parse_blocks(), but since it's based on the blocks used it would only be useful for content built with the block editor.

function wpse_346884_get_suggested_post_format( $content ) {
    if ( ! has_blocks( $content ) ) {
        return null;
    }

    $block  = null;
    $blocks = parse_blocks( $post->post_content );

    if ( 1 === count( $blocks ) ) {
        $block = $blocks[0]['blockName'];
    }

    if ( 2 === count( $blocks ) ) {
        if ( 'core/paragraph' === $blocks[1]['blockName'] ) {
            $block = $blocks[0]['blockName'];
        } 
    }

    switch ( $block ) {
        case 'core/image':
            return 'image';
        case 'core/quote':
        case 'core/pullquote':
            return 'quote';
        case 'core/gallery':
            return 'gallery';
        case 'core/video':
        case 'core-embed/youtube':
        case 'core-embed/vimeo':
            return 'video';
        case 'core/audio':
        case 'core-embed/spotify':
        case 'core-embed/soundcloud':
            return 'audio';
    }

    return null;
}

Then you might want to implement some additional logic to make sure the theme supports the returned post type.