Several problems at once
Despite the fact that Sony recently released the PlayStation Portal portable device, which cannot be called a full-fledged game console, rumors still suggest that a full-fledged pocket console from the Japanese company will indeed be released in the foreseeable future. And supposedly it will be able to run PS4 games. However, experts from Digital Foundry believe that it is precisely the last aspect that is very doubtful.
They believe that it will be very difficult to create a portable console capable of running PlayStation 4 games due to power consumption limitations. In addition, the PS4 has a memory bandwidth of 176 GB/s. This is not much compared to modern consoles, but the same Steam Deck is only 88-102.4 GB/s depending on the version, and even the Asus ROG Ally X is only 120 GB/s, and it uses LPDDR5X-7500 memory.
In addition, such a portable system would require the use of an AMD Jaguar processor for compatibility, and this is too old an architecture.
Of course, a portable PlayStation with a modern architecture will be able to run PS4 games, but they will have to be ported, which will significantly reduce the game library, since not all developers will do this. But such a system will be able to run simplified games for PS5 without any problems.
According to rumors, the portable PlayStation could be released around the same time as the PS6. The console is credited with a GPU with 1152 stream processors, but it is unclear on which RDNA architecture.