In the arc where Sasuke and Boruto time travelled to the past, It was mentioned that Sasuke removed the memories of everyone, well except for Kurama. Did he really forgot to remove it? or Kurama kept it all this time?
..Boruto Episode 136
There is no evidence that Sasuke removed Kurama's memories. So, I believe Kurama knows everything.
I only remember the first time when Sasuke entered Naruto's mind/ the Bijuu Psyche.
Tenchi Bridge Reconnaissance Mission
Sasuke, with his active Sharingan, suddenly appeared within Naruto's subconscious, which surprised both Naruto and the Nine-Tails. The Nine-Tails became impressed with Sasuke's growth and ability, but as it stated that Sasuke's chakra was similar to Madara Uchiha, Sasuke effortlessly suppressed the fox's residual chakra with his Sharingan. Although angrily shocked by the display of his power, the Nine-Tails concluded that this might be its last meeting with Sasuke, so it warned him not to kill Naruto, because he would only end up regretting it.
It simply means that even if Sasuke tried to enter Naruto's mind and talk to Kurama, the beast will not listen because Kurama hates humans and the human he hates most is Uchiha Madara. Also, in many later episodes when Naruto got a lot of control over Kurama, Kurama always used to try to influence Naruto to hate humans of what they did to him. He wants to make Naruto like himself. He also tries to make him remember Sasuke's betrayal every time. So that means even Kurama is unable to recognize Sasuke.
Kurama's chakra is deeply connected to Naruto's chakra so I think any kind of genjutsu used on Naruto will also effect Kurama.