Recent Patch (11/09/21) broke the launcher on my end.
I do have a workaround for it though.
R-click your GW2 Client.
Go to Properties.
Then to Compatibility (should be the bottom R of the 6tabs up top).
Then check off "Disable Full Screen Optimizations"; apply it.
It worked for me after this change - if someone already figured it out, just take this as an extra confirmation.
Amusingly though, it acts like it has fullscreen anyways 🤣.
I've had the Client break on my end in the past as well - resolved those by uninstalling/reinstalling the Client (if the above fails).