Personally I think you are battling the wrong thing. A single specific console being allowed or banned won't make or break a child's addiction or unhealthy gaming habits.
If he had no devices at all, and you were arguing about introducing his first console or not, that would be different - but here we are talking about adding a new device, to the list of game-ready devices he already has.
For someone who likes gaming (as I did a lot back when I was younger and had plenty of time) if you want to game, you will game on whatever you have. Only have a basic laptop? no problem, there are plenty of online browser games that will run on anything.. phones, plenty of games etc. Refusing to buy one specific console won't stop him gaming or make him not have an issue with time management/gaming addiction.
Yes a new console will fuel a short-term increase in his gaming, as with any new purchase, the excitement of the first weeks/months is a lot, but long term, it likely won't increase or decrease his desire to game.
The battle you should be fighting is the type of game he plays, and how he plays it. The research on video games is fascinating - they aren't universally bad. In fact some are great, and actually help facilitate problem solving, logic, concentration etc. However, others do the exact opposite and are dangerous addictive time-traps.
Focus on teaching him the role gaming has in his life, and make sure the choice of games is positive, instead of banning/prohibiting things outright. He is old enough now to learn those rational-thinking skills, and you'll avoid the issue of banning something making it just even more desirable.
For me, I'd let him have the console but on the condition that it conforms to your existing screen time rules, and with the extra condition that you get final say over what games he buys or plays until he is older.