OK, so that generates links to date archives.
And you can use a PHP Snippet to set the cat query to the ID of a single category:
function exclude_category_from_archives( $query ) {
if ( $query->is_date() && $query->is_main_query() ) {
$query->set( 'cat', '99' );
}
}
add_action( 'pre_get_posts', 'exclude_category_from_archives' );
Replace 99 with the id of your category.
NOTE: This will not change what the calender displays, that is a core Block, and they did not add any filters hooks ( to my knowledge ) to change what it displays.