On iPhone, if you are in the “Messages” app, at the top left hand corner, click on the
<
(left hand pointer), multiple times if needed, until you see the
< Fliters
Once you click on the left hand pointing arrow next to the word filters, you should then see a list of :
All Messages
Known Senders
Unknown Senders
Unread Messages
So, there you can click upon ‘Unread Messages’ to ONLY show you un-read messages.
Additionally, once you are looking at your Unread Messages, you can also click upon the little circle with 3 dots in it to the right of the word Unread at the top, choose ‘Select Messages’, and then at the bottom left, click on :
Read All
That should result with ALL messages being marked as read.