Your device and/or the app may be a slightly different version than what you had before.

This happened to me before, when I had a device replaced with an 'identical' device under warranty.

The solution, if needed at all (you have already found a workaround) is possibly to clear the defaults for the camera app.

The next time you try to attach something, the screen asking which app to draw the attachment from should appear.

 

Most likely answer is an app update, to be honest. I don't use Messages, prefer other SMS apps, but I just tested it on my Pixel 2 and it's as you describe: touch the "+" icon to add media to a message. So I expect that's just an update to that app's UI, and the way it is now.