There's not even a new COD that's been announced yet, and an exclusive COD won't be here for another 2 - 3 years. The people you're talking about will be staying on last gen for a while still
2023 COD could be exclusive to Xbox if the sale goes through as expected. Sony only have a marketing rights agreement, for all we know it has clauses in it for sale of the franchise etc. We don’t know, and we won’t find out until the sale is approved and completed. Just because a game was going to release on a console doesn’t mean that it contractually has to release on it. Again, Starfield is the latest example. We know Sony were trying to buy timed exclusivity, but now they’re not even getting the game even though the development was well underway of that version.
What I’m saying is that a sale of the company changes everything. Once that happens everything is up in the air. We just have to wait and see. Going by the entire history of the gaming industry, and the recent Bethesda acquisition, anything not secured in a timed exclusivity contract by Sony will not release on PlayStation.
Marketing rights deals are not the same as timed exclusivity, so we don’t really have any precedent here that I can remember. Maybe someone else knows of a situation like this that has happened before?
I doubt tens of millions of PS5 owners will jump ship to Xbox as soon as cod goes exclusive, but they’re not the people Microsoft are going for - they’ll be gunning for the 150 million people that will buy a console after that day, and having cod exclusivity gives them a huge leg up.