Did Naruto and Sasuke receive the Sage of Six Path's chakra or Asura's and Indra's chakra? So Naruto already has Asura's chakra, and Sasuke has Indra's chakra. Did the Sage of Six Paths give them his own chakra? Or did he give Indra's chakra to Naruto and Asura's chakra to Sasuke which fused together to make his own?
The Wiki only states that Hagoromo gave Naruto Six Paths Yang Power and gave Sasuke Six Paths Yin Power. That's not the chakra specifically, but rather a technique. Although there was some chakra transference involved.

Hamura, Hagoromo's brother, only had Six Paths Yin Power and Hagoromo's children didn't have either.
Indra had Yin Release and Asura had Yang release but they didn't have anything like the power given by Hagoromo to Naruto and Sasuke. I know you didn't claim that Asura and Indra had these powers but I'm just stating that these two powers Naruto and Sasuke received aren't in the same context as their reincarnated power. Hagoromo did give these powers to them because they are Asura and Indra reincarnated but the power didn't develop in them because of this, it was given to them whole by Hagoromo.

The "fusing" of chakra you mentioned was only demonstrated in Sasuke's left EMS turning into a Rinnegan, but I'm not sure if was blending of chakra or simply because he received half Hagoromo's power, so he gets half of his eyes turned into Rinnegan. This last part is highly speculative, though.