Have you tried running Firefox in a safe mode to see if it is related to any extensions you might have? I would try Chrome too just to isolate it to the browser or Vortex or something in between. If it works in Chrome then you know the problem is probably Firefox configuration. If it doesn't work in Chrome, it's related to either your Vortex config or something in Windows that isn't allowing apps to be linked from the browser. I don't know too much about how that works.
Also I've re-installed Vortex on top of an existing install several times and it does not wipe anything. It probably does not fix any problems either but harm does not come of it. If you want to a deeper wipe and re-install, like delete everything Vortex and try again, I notice there is a database backup feature in Vortex settings, not totally sure what it does but I think it allows a backup and restore of your metadata.
You probably already know but if your Vortex login has timed out, it doesn't really tell you that but it does time out, Vortex links from the Nexus will no longer work but they do throw an error (perhaps you are not seeing it for some reason). The top right ellipses in Vortex has an option to "refresh user info" that will log you back in. I often have to hit that first if I haven't downloaded in an hour or so, or the Nexus Vortex links will not work.