how to delete all users and posts based on ‘user_meta’?

Because “institute” is a user and you want to perform some actions when it is deleted, you could use delete_user action (as we need information of the deleted user, deleted_user may not work, not sure about this but delete_user should work for sure). In that hook you can get all users and posts based on inistitute_name meta field and delete them.

Seeing your code, “Institute” user type can be identified by user role (you assing admin) and user meta inistitute_name. So, in delete_user action you can check if the deleted user is and admin and if it has institute_name assigned, in that case, the deleted user is a “institute” and you can get all other associated users and posts.

add_action( 'delete_user', 'cyb_delete_institute_info' );
function cyb_delete_institute_info( $id ) {

    $user = get_userdata( $id );

    if( ! empty( $user ) && in_array( "admin", (array) $user->roles ) ) {

        // Deleted user is admin, check `inistitute_name` meta field
        $institute_name = get_user_meta( $id, 'inistitute_name', true );

        if( ! empty( $institute_name ) ) {
            // Deleted user is an admin and has `institute_name` meta,
            // so, it is a "Institute" user

            // Get posts to delete
            $posts_args = array(
                'post_type' => array( 'courses', 'notifications' )
                'meta_query' => array(
                    'key'   => 'inistitute_name',
                    'value' => $institute_name
                ),
            );

            $query = new WP_Query( $posts_args );
            $posts_to_delete = $query->get_posts();

            foreach( $posts_to_delete as $post ) {
                wp_delete_post( $post->ID );
            }


            // Get users to delete
            $users_args = array(
                'role__in'       => array( 'trainer', 'trainee' ),
                'meta_query' => array(
                    'key'   => 'inistitute_name',
                    'value' => $institute_name
                ),
            );
            $query = new WP_User_Query( $users_args );
            $users_to_delete = $query->get_results();

            foreach( $users_to_delete as $user ) {
                wp_delete_user( $user->ID );
            }

        }

    }
}

Note: not tested, just written here as sample code.