See you're having some trouble with the launcher, I have a few steps here that may help you:
1) UninstallParadox Launcher v2 in Add/Remove Programs, then relaunch the game. Stellaris will redownload the launcher. You should wait for it to download the update, close and relaunch the launcher before trying to start the game.
2) Some launcher issues are caused by conflicts with antivirus active protections, like AVG or Avast. Add Stellaris/Paradox Launcher v2 to the exceptions list to any antivirus program you're running with active protections.
3) If all of this doesn't work, go to
support.paradoxplaza.com and open a ticket, and customer support will be able to help you with this issue.
Hope this helps!