Um why aren't you asking this about Raki and Touya though too? I mean they're reincarnated forms are Kou and Kazumi just as Ren/Garai's is/are Jun and Hazuki.
ummm because they've already been reincarnated just not completely...neither Jun nor Hazuki has made a contract or inherited the soul of Garai...since he was destroyed/set free. Raki hasn't synced 100% which is why he has no memories but he has the power and made the contract, same as Touya except he's more in sync w/ complete memories and more power. SO the only question is about Garai whose soul was corrupted, since Hazuki achieved his power through force he wasn't accepted and Jun has shown signs of some memories (knowing the faces of the Warriors) but no powers since he was supposed to be the vessel. As you said they're already reincarnated..
Except my point is that they were already reincarnated long before they made the contract. Besides the reason the contract is corrupt in Tarupa's case is because of the way Hazuki received the contract. After all as Kou, and then later either Shana or Ruou, clarified the contract is made when the Shinma warrior surrenders everything to the Divine Beast, which is why as one of the latter two had also mentioned it had taken so long for Touya to reappear after the last Touya had died. Because of course surrendering everything everything to the contract includes surrendering their very lives. Which means the Shinma warriors existed before the contract was made ofc. That's just my thoughts though.
so does that mean Garai won't reincarnate?? Since his soul was corrupted and they freed him is that it or does his soul go back through the whole process again? Cause where is that going to leave Hazuki and Jun. I'm super curious as to how this is going to work out