How to extend SelectControl with data from my theme

You can use wp_localize_script() to pass JavaScript variables to the editor:

$asset_file = include(get_template_directory() . '/path/to/blocks/index.asset.php');

wp_register_script(
    'pb-theme-blocks',
    get_template_directory_uri() . '/path/to/blocks/index.js',
    $asset_file['dependencies'],
    $asset_file['version']
);

wp_localize_script(
    'pb-theme-blocks',
    'pbThemeBlocksVars',
    array(
        'classes' => array(), // Your theme classes go here
    )
);

Then in your edit function:

const classes = pbThemeBlocksVars.classes;