It’s definitely better to use the system web view. Including all of WebKit in the static binary is clearly not a good option. I think the easiest solution would be to document the dependency, and to have a better error message than just getting the “No such file or directory” from the linker.
I’d mention that WebKit2GTK is very much specific to GTK. The equivalent used on QT based desktops like KDE is QtWebEngine (or QtWebKit? (it’s a bit confusing)).