The current user interface for copying and pasting text is very annoying in Web Access. Instead of just doing it directly you have to go via a special text field that you open from the control bar. The reason it is built like this is because the browsers have restrictions in place for how JavaScript can access the clipboard. However new JavaScript APIs are available (and more on the way), so perhaps there is room for improvement.
Until the new APIs are in place, perhaps things can be simplified with two sync buttons like NICE DCV has solved this: https://github.com/awsdocs/nice-dcv-user-guide/blob/master/doc_source/using-copy-paste.md
Upstream issue for this: https://github.com/novnc/noVNC/issues/1511
