When the PS5 actually gets announced or gets some heavy rumors, I'll call that 'next-gen'.
Until then, everybody knows exactly what somebody means when they say 'next gen'. This is how language works. So long as I, and millions of others, call something 'next gen' and people know what we're referring to, it is *correct* phrasing.
No amount of your asinine literal pedantry will change that, sorry. Get over it. Next-gen = XB1/PS4. Just the way it is. You cant argue your way out of it. The best you can do is say it means something different to you, but you cant change the way language works for everybody else, I'm afraid.