As far as I'm aware your unable to mark a text message you've read to then unread.
If I'm right then I'd suggest to send this as feedback via your Samsung Members App under the GetHelp section.
Daily Driver > Samsung Galaxy s²² Ultra 256Gb in Phantom Black.
The advice I offer is my own and does not represent Samsung’s position.
I have no affiliation with Samsung.
@ZFoldNovice: As a possible workaround for your issue, please head to the Messages app > Press and hold on the relevant message > Tap the 3 dots in the bottom right > Pin to top. As new, unread messages are shown at the top of your Messages inbox by default, this will be a good way to keep them visible for ease of access.