UPDATE 29/4/21: Ahead of its annual 4th May marketing event, Disney has confirmed the upcoming PlayStation 5 and Xbox Series X/S versions of Star Wars Jedi: Fallen Order.
The new editions will arrive this summer with various technical enhancements, and be offered as a free cross-generation upgrade to existing owners on PS4 and Xbox One. More details on exactly when and what has changed will be announced on a date not too far, far away.
ORIGINAL STORY 18/3/21: Star Wars Jedi: Fallen Order has already received a next-gen optimisation patch to improve how the game runs on new hardware, but it seems a native next-gen version could also be on the way - according to the German ratings website, at least.
As spotted by Gematsu, the German USK games rating board has now listed a PlayStation 5 and "Xbox" version of Fallen Order. These are new listings that appeared on 2nd March, and can be seen here alongside older listings for PC, PlayStation 4 and Xbox One.
Fallen Order initially got a surprise next-gen patch back in January, which essentially tweaked last-gen code to improve performance on Xbox Series X/S and PS5. The patch mainly focused on improving frame-rates, along with post-processing quality and increased resolutions. Digital Foundry tested the patch and found that it was certainly an improvement, with the game running at a fairly steady 60FPS on both systems, but some problems remained with hitching and stuttering. Hopefully some of these problems can be ironed out in future.