Hmm, you shouldn't have to go through such an elaborate process. When you send a text to someone, there should be an Attach button that allows you to select a photo to attach.
In Step 3 that you showed in those screenshots, when you tap the icon with the speech bubble (which is the Start Conversation button), what do you see? I'm assuming you're first asked to choose a contact(s) to send to, after which you should see a text entry field to type your message. That text entry field ought to have an Attach button. Can you show us a screenshot of that?
I don't use the Samsung Messages app (I have a Pixel 7 Pro, so I'm always on Google Messages), so I can't test things out reliably. It might help to have
@mustang7757 in this thread as well.