Everyone can write a new version of the GPL.
The standard GPL permission statement explicitly clarifies that the license is “as published by the Free Software Foundation” so any later version of the license has to come from the FSF.
This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.
The reason for the “or later” clause is to allow the FSF to update the GPL in response to flaws that are discovered. The “or later” clause is controversial because it effectively allows the FSF to change the licensing terms of any software licensed under such a clause, and so some developers who don’t trust the FSF with this authority omit this clause. Famously, Linux is licensed only under GPLv2 with no or-later option (Linus has been a vocal opponent of GPLv3)
Vivaldi’s target audience is people who don’t mind proprietary blobs as long as they are “good” or make things “work better.” Given that Vivaldi itself is essentially a proprietary blob combined with a Chromium backend this makes sense.