For all the years I used on my desktop it was just C-a-<key> however on this laptop install it wants C-a-Shift-<key>.

The only other time I experienced this behavior is when I would ssh into remote machines and you could access nested screens. So if I was in screen on the desktop sshing into remote I could then do screen in that one and then it would require shift to move around in the nested screen on the remote machine. Not sure why it is happening on the laptop now.

Also on desktop when you enter copy mode for example with C-a-Escape it will show a message at the bottom to indicate you entered copy mode yet when doing so on laptop it shows no messages.

I am wondering if the issues are related.

I have no idea, but it would be interesting to drill down on the details.

Is your caps lock off? :-)

Which version of screen is it? Do you have another device where screen is working as expected? Which version is it there?

Have you tried building screen from source code and installing it in $HOME/local/? Does it behave the same?

Do you have a $HOME/.screenrc? If so, what's in it? What's in /etc/screenrc?