You might want to try to send ctrl+c (using something like xdotool or ydotool) to the app to copy the current selection to the clipboard and then to extract clipboard contents to use it in a script.
Thanks again. I changed my Klipper configuration (the KDE clipboard application) to synchronize selection and clipboard. In addition, I added a global shortcut (F1) to execute this little script:
It reads the clipboard (equal to the current selection) via wl-paste and sends a request to the Claude API via curl. Finally, it filters the response with jq (very crude) and displays it with notify-send. I have a second version of the script that sends the result via XMPP to Gajim because the answers can be quite long.
I think the experience should be similar to the one on MacOS.
After so many years, Wayland is still such a mess...