Rockstar clarified the problem
One of the biggest games in this decade, Rockstar Games next masterpiece, Red Dead Redemption 2 just released today. After the release, almost every corner of the internet is filled with news, guides, screenshots, and gameplay videos of the Red Dead Redemption 2. But let's get back into topic. The players who purchased the Ultimate Edition of the Red Dead Redemption 2, reported that they cannot download the Ultimate Edition bonuses of the game while they are trying the download these DLC.
But today, Rockstar Games officially clarified this question. From their official support article, they said:
Question: I pre-ordered the Ultimate Edition of Red Dead Redemption 2, but why does the game say that I only have the Special Edition on PlayStation 4?
Answer: While the installed game may appear to be the Special Edition, all Ultimate Edition in-game bonuses and content are associated with your player profile and will be available when Red Dead Redemption Online launches.
So if you purchased the Ultimate Edition of the game and didn't see the bonuses, do not worry. You will get your bonuses when Red Dead Online opens its doors.