It needs custom code to achieve this.
If you have PHP knowledge then i can direct you.

Use following filter hooks and unset $args['mgs_type'] and add $args['mgs_type_in'] = [ 'message', 'announcement' ]

fep_message_count_query_args
fep_message_query_args
fep_filter_get_message_with_replies

(Untested)

Please do not change plugin code as this will be lost when you update.
You will need to use those 3 filter hooks to execute. To know more about hooks please see https://developer.wordpress.org/plugins/hooks/filters/

If you need custom code help you can contact via https://www.shamimsplugins.com/hire/

Message and Announcement works in different way and they are queried also in different way.
So you will have to change so many filters to works it properly. Also some information for messages and announcement is different in database.
It will not be small amount code which i can provide you.

Message and Announcement works in different way and they are queried also in different way. So currently it is not possible to combine them.