While there have been rumblings about limited PS5 availability at launch, we've had no such rumors about the Xbox Series X and both consoles appear to still be on target for the "Holiday 2020" launch.
What is considerably less certain, is the status of the launch titles for the consoles according to a CNBC interview with Microsoft's executive vice president of gaming and head of Xbox Phil Spencer (via The Verge).
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Spencer expressed confidence that the hardware launch was "in line with where we thought we would be," but followed that up by saying that the "bigger unknown is probably the game production."
We know we are finally going to see some Xbox Series X gameplay next week, but this naturally doesn't tell us much about these games' viability to ship in time for the launch. While The Last of Us Part II is finally expected to ship in June, the game was delayed considerably due in part to the impact of Covid-19. It's hard to predict what the impact will be for games that were still roughly half a year away from launch.
Xbox Studio Games notably aren't expected at the gameplay event next week with a separate event later in the summer likely for those, but that does leave open the question of where they stand given that Spencer certainly is well aware of the status of those teams.
The Xbox One and PS4 both launched with 23 games available with right around 30 games available within a few months of launch, there are only a few confirmed launch titles for either next-gen console at the moment, so we will be paying very close attention to what's said at the events over the coming months to see if either will come close to that total for the launch of the Xbox Series X or PS5.