Horizon Forbidden West will not offer a free upgrade from the PlayStation 4 to PlayStation 5 on either its Standard or Special Editions. You also cannot pay to upgrade from the Standard edition to an edition that does include the PS5 upgrade either.
As it currently stands, PS4 and PS5 will receive totally separate versions of the same game. You will be able to play the PS4 release on the PS5, but it won't have any of the PS5 specific visual and performance...